Sen. Rob Portman (R-Ohio) speaks with reporters at the Capitol in May. (AP)

Tuesday’s announcement that the 2016 Republican National Convention will be held in Cleveland underscored the importance of Ohio in the party’s national strategy to win back the White House and affirmed the influence of Sen. Rob Portman, who pushed for months for the lakeside city to land the coveted nominating convention.

But Portman (R-Ohio) is interested in more than just hosting the convention in his home state. He would like a starring role, perhaps as his party’s presidential nominee.

“I’m not particularly eager to do it myself, and having been involved in six presidential campaigns, I know what it’s like,” he said in a recent interview in his Capitol office. “But if nobody running is able to win and willing to address these issues, then I might have a change of heart.”

Acknowledging a flurry of encouragement from 2012 GOP nominee Mitt Romney and powerful insiders, as well as his own burgeoning ambition, Portman said that he has been contemplating a 2016 presidential bid for some time and that he may be uniquely positioned for such a run.

Portman’s swing-state roots, years of legislative and executive experience, and support for same-sex marriage could provide him with a singular space in the field and make him a favorite of the Republican Party’s establishment, especially if former Florida governor Jeb Bush decides to sit out the race.

Portman, 58, who endorsed same-sex marriage last year after learning that his son Will is gay, has focused this year on crafting an anti-poverty agenda and making his case with a notably softer tone than the one now associated with his party’s hard-liners. Speaking at the American Enterprise Institute in May, he backed efforts to index the federal minimum wage to inflation and said bipartisan prison reform and empathy for nonviolent drug offenders should be GOP priorities.

Portman is confident that his position on gay marriage has not crippled his ability to be a national candidate, arguing that it has enabled him to connect with the young voters his party is struggling to court as it grapples with changing demographics. When they find out that he supports same-sex marriage, he said, many shed the antagonism they usually reserve for Republicans.

“It has opened the door for a broader conversation on economic and fiscal issues,” he said. “You can’t become a national party unless you do a better job reaching those between 18 and 30. They are the voters of tomorrow, and we want them to listen to us on jobs and Obamacare.”

Portman, a Methodist who holds antiabortion views, said most rank-and-file Republicans are aware that, on issues other than marriage, he has been a staunch social conservative throughout his career, from his election to the House in 1993 to his current term in the Senate, to which he was elected in 2010.

“Some people say: ‘I don’t care about that. I care only about the marriage issue.’ And I get that,” he said. “But we’ve got to show respect for both sides. Respect is important — respect for people’s religious views, respect for personal experience. It should be a sincere and healthy dialogue.”

Portman’s talk of a possible presidential campaign comes as Bush continues to signal hesi­ta­tion about whether he wants to return to public life after nearly a decade away. Another leading potential candidate from the GOP’s center-right wing, New Jersey Gov. Chris Christie, is struggling to recover his once-soaring popularity among prominent donors after a bridge-closing scandal.

Speculation about a Portman run has increased as he, in his role as vice chairman of the National Republican Senatorial Committee (NRSC), has traveled the country to meet with party figures and wealthy conservative financiers, including hedge fund manager Paul Singer.

Singer shares Portman’s position on same-sex marriage, and Romney has signaled to his allies that Portman, despite his relative obscurity, is one of several contenders with the profile to be a viable standard-bearer.

Last month, Portman attended Romney’s invitation-only retreat in Park City, Utah, mingling with high-placed attendees, briefing donors on the Senate map and leading a group on a mountain-bike ride.

In a phone interview, Romney praised Portman, who was on his short list for the 2012 vice-presidential nomination. He said the senator would be a “very credible candidate if he chooses to take that step.”

“Rob has demonstrated a kind of practicality that is appealing,” Romney said. “There is a stream in my party that is anxious to fight but not as concerned with winning, and I think that’s the minority stream. I don’t think that kind of Republican is going to be the nominee. I believe the nominee will be a mainstream, practical Republican who has the capacity to go through a nominating process that could go quite a long distance.”

Portman, however, is far from building a national political apparatus, and his trips to early primary states have been limited to New Hampshire, where his daughter attends his alma mater, Dartmouth College. While his stance on marriage and fiscal conservatism could play well in the Granite State, he has a low profile there — he tied for last in a March survey of Republicans attending a conservative event.

Most of his networking is done on his own — he personally lobbied Republican National Committee members on Cleveland’s behalf — or through his tightknit inner circle, led by chief of staff Rob Lehman and longtime adviser Joe Hagin, a childhood friend who served as a top aide to President George W. Bush. Stuart Stevens, who served as Romney’s top strategist in 2012, is another confidant.

Portman said he would not make a final decision until later this year or early 2015. As a close associate of the Bush family and one of Christie’s key Republican contacts in the Senate, he is sensitive to the deliberations of Jeb Bush and the New Jersey governor. He said he is simply beginning to explore the idea and intently watching how the pre-primary jockeying unfolds, all while urging the GOP “to build a bigger tent” and assisting Senate candidates with fundraising and messaging.

“Let’s see what happens. Let’s see who runs,” Portman said. “For the moment, I’m up for reelection in Ohio, so that’s my plan.”

A Portman candidacy would be notable not just for his break with the party line on gay marriage but also for his lengthy Beltway résumé and the widespread goodwill from the GOP’s political class that he would bring to the race.

After graduating from the University of Michigan Law School, Portman worked in President George H.W. Bush’s White House. He still travels to Kennebunkport, Maine, most summers to visit with the former president, whom he considers his mentor and an exemplar of the pragmatic, tradition-bound Republicans he admires.

After serving in the House for six terms, Portman was tapped by George W. Bush to serve as U.S. trade representative. He worked in that position from 2005 to 2006, negotiating trade agreements with South Korea, Colombia and Panama and ushering the Central American Free Trade Agreement through Congress. He spent the following year as director of the Office of Management and Budget.

Portman’s Bush ties are a mixed blessing, giving him access to the one of the most entrenched and formidable power bases in the party but also linking him to George W. Bush, who has become a target for tea party activists. When Portman was mentioned as a possible vice-presidential nominee in 2012, some said they disapproved of Portman because the federal deficit increased during his time as budget director. His stint as a trade lawyer for Patton Boggs, a law and lobbying firm in Washington, has also bothered them.

Portman, in response, has frequently said that he tried to curb spending increases while working in the last Bush administration and proposed a balanced budget in 2007.

Working at a senior level on presidential campaigns, from George H.W. Bush’s 1988 run to Romney’s 2012 campaign, has been critical to Portman’s ascent, and he has carved a niche over the past two decades as a master of debate prep, guiding Republican nominees before televised showdowns and impersonating Democratic nominees.

In the Senate, Portman has a reputation as a cloakroom operator, cozy with party elders and forging relationships across the GOP divide. In 2011, in the chamber for less than a year, he was selected to be on the “supercommittee,” a bipartisan panel on deficit reduction. During last year’s immigration debate, supporters of a comprehensive overhaul wooed him for weeks, knowing that as a Spanish speaker — he learned it while working on a ranch in Texas as an undergraduate — and as a relative centrist, he was interested. But Portman, citing concerns about border security, ultimately voted against the package.

Portman’s reelection campaign has nearly $5 million in cash on hand, and he has raised more than $11 million for the NRSC this cycle.

“To win a national election, we’ve got to work on fixing the Republican brand, and that’s what I’ve been working on,” Portman said. “We’ve got to be the party of ideas, not the party of no. . . . The Democrats have successfully mischaracterized Republicans in many instances, and that’s why Mitt Romney had a tough time winning Ohio. They called him a plutocrat without compassion.”

Ohio has a history rich with presidential intrigue. During the 19th and 20th centuries, seven Republican presidents called Ohio home, from Ulysses S. Grant to Warren G. Harding. Sen. John W. Bricker was the GOP’s vice-presidential nominee in 1944. Sen. Robert Taft, a conservative star dubbed “Mr. Republican” whose portrait hangs in Portman’s office, challenged Dwight D. Eisenhower for the Republican presidential nomination in 1952.

Cleveland and Dallas were the RNC’s two finalists for the convention selection, and Cleveland is also one of six cities competing for the Democratic National Convention. Obama won Ohio in 2012 and 2008. George W. Bush won the state in 2000 and 2004.

On a conference call Tuesday afternoon, Portman said Ohio is the “right state for it, the heartland” and the keystone to the GOP’s presidential chances. When asked whether it may be so for his own chances as well, he did not dismiss the suggestion.