WASHINGTON, DC - MAY 23: U.S. Trey Gowdy (R-SC) (L) speaks during a hearing before the House Permanent Select Committee on Intelligence on Capitol Hill, May 23, 2017 in Washington, DC. Former Director of the U.S. Central Intelligence Agency (CIA) John Brennan testified on the extent of Russia's meddling in the 2016 U.S. presidential election and possible ties to the campaign of President Donald Trump. (Photo by Alex Wong/Getty Images) (Alex Wong/Getty Images)

The House’s most powerful investigative gavel is set to land in the hands of Rep. Trey Gowdy (R-S.C.) with little drama once Oversight and Government Reform Committee Chairman Jason Chaffetz leaves Congress next month, according to multiple members and aides familiar with the behind-the-scenes discussions about the post.

Chaffetz (R-Utah) is stepping down June 30 to pursue a private-sector career amid sharp public focus on the Republican Congress’s willingness to conduct oversight on President Trump and his administration.

Gowdy, who led the two-year House Benghazi probe, has secured near-unanimous support among members of the House Republican Steering Committee — the 36-member body that selects committee chairmen — and one key potential rival said Monday that he would not seek the Oversight gavel.

“I have not been making a play, and I’m not going to,” Rep. Jim Jordan (R-Ohio) said Monday. “Look, you guys know how this works: The establishment’s not going to put the anti-establishment guy in charge of the committee whose job it is to go after the establishment.”

Jordan did not express opposition to Gowdy becoming chairman.

“I think Trey’s probably going to be our guy, and Trey’s a good guy,” he said.

Jordan is a longtime member of the Oversight panel and has more seniority than Gowdy. But he has staked out a reputation as a conservative firebrand willing to buck party leaders on high-profile issues, co-founding the House Freedom Caucus to gather fellow iconoclasts into a powerful voting bloc.

As Jordan acknowledged, there was little chance that the party pooh-bahs who sit on the Steering Committee would entrust one of the institution’s highest-profile positions to a member known for acting independently of GOP leaders.

But Jordan could have pressed the issue, enlisting supportive Oversight panel members to back him and undermine Gowdy, and several Freedom Caucus members said in recent days that they were ready to go to the mat for Jordan.

“Here’s a guy who’s been very dynamic on the committee, he’s very organized, and he identifies with people across the country,” said Rep. Paul A. Gosar (R-Ariz.), a Freedom Caucus member who sits on the Oversight panel. “Not that Trey doesn’t, but he’s been the center focus of [Oversight and Government Reform] from Day 1.”

Gowdy declined to comment on his interest in the Oversight post last week. Spokeswoman Amanda Gonzalez said Tuesday that Gowdy “is continuing to speak with members in the conference about the qualities they believe are most important for the next Chairman to possess.”

But several Steering Committee members said privately that Gowdy had assured them he is willing to serve and that had the post all but wrapped up, thanks to his background as a criminal prosecutor, his high-profile stint as chairman of the select committee that investigated the 2012 attacks on U.S. outposts in Benghazi, Libya, and his reputation as a well-liked team player inside the House GOP conference.

“Trey’s proven himself over the last several years with the difficult roles he’s accepted, and clearly his history and his background perfectly suits him for this chairmanship,” said Rep. Tom Graves (R-Ga.), a Steering Committee member who said he plans to nominate Gowdy when the body meets next month. “He’s got the trust and the confidence of our conference, and he’s going to do a fantastic job.”

Other members spoke on the condition of anonymity to describe private conservations with Gowdy and other candidates.

Another Oversight Committee member, Rep. Dennis A. Ross (R-Fla.), approached House leaders about possibly running for the chairmanship before throwing his support behind Gowdy. “He’s got the credibility. He’s got the expertise,” he said Monday. “He knows the jurisdiction of the committee very well, having served on it for six years. And he can do the legislation that’s necessary.”

After enduring months of criticism for not moving more decisively to investigate ethical questions about President Trump and his business ties, Chaffetz moved in recent weeks to have panel Republicans examine Trump’s alleged efforts to derail a federal probe into Russian connections to his administration and campaign.

Chaffetz invited former FBI Director James B. Comey to address the committee this week about his interactions with Trump before his firing earlier this month. That appearance was canceled, however, due to concerns over whether Comey’s testimony might impede the parallel Justice Department probe.

Gowdy is already familiar with the questions over Trump’s Russia ties due to his seat on the House Permanent Select Committee on Intelligence, which has conducted a probe of its own since allegations of Russian efforts to influence the presidential election surfaced late last year.

That panel hosted former CIA director John Brennan on Capitol Hill Tuesday, and Gowdy sharply pressed Brennan to share evidence of connections between the Trump campaign and “Russian state actors.”

“How did you test, probe, examine, cross-examine, otherwise test the reliability or believability, credibility, of that evidence you uncovered?” he asked at one point, questioning whether the CIA assessment of Russian interference was reliable.

While Gowdy has broad support for the chairmanship, he is not running unopposed: Another Oversight Committee member, Rep. Steve Russell (R-Okla.), is also seeking the job.

Russell, a second-term former Army infantry officer, is respected among House Republicans but does not have quite as deep a reservoir of support among steering committee members.

In an interview Monday, Russell said that while Gowdy is a friend and is impeccably credentialed as an investigator, he had a strong record on the “government reform” side of the committee’s portfolio.

“If I can lead a 1,000 soldiers in battle, I can probably lead a committee,” said Russell, who retired as a lieutenant colonel, adding that he did not want the panel “to return to the very divisive polarizing days that we had in years past.”

Russell said he was running with Gowdy’s encouragement and suggested he was mainly seeking to raise his profile in anticipation of a future vacancy.

“I’m very aware of what goes on behind those closed doors, but I think it’s also important to provide a depth of bench,” he said. “Do we honestly think that we will not be facing this problem again in a couple of years? Mr. Gowdy is in high demand. If there were a federal prosecuting job or something of that nature that were to come along, then rightfully so it would be of great interest to him.”

“I have a long history of people underestimating me,” he added. “You get nothing if you do nothing.”

House GOP leaders announced last week that the Steering Committee will convene early next month, during the week after the Memorial Day congressional recess, to select the new chairman.