James Shields of the Tampa Bay Rays is a potential trade target for the Nationals. (J. Meric/GETTY IMAGES)

The Washington Nationals need a fifth starter, but here’s the thing about General Manager Mike Rizzo: He doesn’t do fifth starters, at least not in any conventional sense. Other teams in need of a No. 5 starter may look for innings eaters or junkballers or any lefty with a pulse. Rizzo looks at his four twenty-somethings with oppressive stuff and wants another to complete the set. He does not want his fifth starter to be a Fifth Starter.

On the opening Monday of the winter meetings at the Gaylord Opryland Hotel, the Nationals continued their search for their kind of fifth starter, one to replace free agent Edwin Jackson. Washington’s front office spent Monday sending feelers to both other teams and agents for starting pitchers on the market.

“We’ve done a little bit of both,” Rizzo said. “We’ve touched base with some agents. We’ve touched base with some teams. Just the general conversations is what we’ve done so far.”

The Nationals have started to narrow their focus, but they have not yet identified their primary target. Rizzo, at this point, has no particular criteria in mind in his search. He said he wants simply to acquire, “the most impactful guy that we can get.”

Rizzo gave the Nationals backup options and depth. Monday, they re-signed Zach Duke to a one-year, major league contract. Duke, who went 15-5 with a 3.51 ERA at Class AAA Syracuse last year, will likely replace Tom Gorzelanny as the Nationals’ long left-handed long reliever. But Rizzo said Duke will work as a starter in spring training to give the Nationals extra depth. Christian Garcia, outstanding in relief last season as a September call-up, will also take on a starter’s workload in spring training.

Either Duke or Garcia starting the year in the Nationals’ rotation would mean something has not gone to plan. When Rizzo says he wants an “impactful” starter, there is reason to believe him. Last winter, the Nationals packed their rotation with six capable starters by the end of January . . . and then gave Jackson $11 million to throw his high-90s heat for one year.

Rizzo will not let the conventions of a fifth starter limit his search for a starter. As such, the two pitchers the Nationals are most enamored with are the two at the top of the class: free agent Zack Greinke and potential trade target James Shields of the Tampa Bay Rays.

Both would require enormous costs to acquire, cash in Greinke’s case and quality players in Shields’s. The Nationals may find the price too high and move on. But they will test the waters for both.

The Rays are the rare team with a surplus of starting pitchers, they desperately need offense and Shields’s contract is set to become expensive for their small-market budget. “I’ve come to grips it may happen,” Rays Manager Joe Maddon said. Shields, a 31-year-old workhorse, will make $9 million in 2013 and has a $12 million team option for 2014.

Shields would be a perfect match with the Nationals’ four young fireballers — Stephen Strasburg, Gio Gonzalez, Jordan Zimmermann and Ross Detwiler. Shields has been a leader on the Rays’ young staff for years — “the best teammate I have ever seen,” Maddon said. He will still be in his prime, or at least the back end of it, for the next two seasons. Over the past six years, he has averaged 222 innings per seasons while punching up a 3.80 ERA.

The cost to acquire Shields would be steep, but the Nationals possess pieces the Rays would find attractive. Michael Morse would become expendable if the Nationals re-sign first baseman Adam LaRoche, and the Nationals could discuss second baseman Danny Espinosa in trade talks. The Nationals could then make Steve Lombardozzi their second baseman, with the possibility of top prospect Anthony Rendon giving the Nationals more infield depth later in the season or in 2014.

Conceptually, dealing Morse and Espinosa for Shields works for both sides. In reality, talks between the teams about the deal have gained no momentum and seem unlikely to result in anything. Some in the Nationals organization would trade Espinosa with little hesitation and play Lombardozzi at second, but Rizzo and Manager Davey Johnson are major advocates for Espinosa. One Nationals official doubted any deal would happen because the Rays are “hard to work with” on trades.

Rizzo’s interest in Greinke is long-standing. In December 2010, the Nationals put the framework of a trade in place to acquire Greinke from the Kansas City Royals. Greinke met with Nationals ownership and Rizzo at a secretive meeting near the winter meetings in Orlando, and the Nationals prepared to offer him a $100 million contract.

Before they could complete the trade, Greinke turned down the offer, believing the Nationals would not contend if they parted with the talent necessary to bring him to Washington. Even though Greinke ultimately shot down the Nationals, the meeting left him feeling good about Washington.

“It wouldn’t have gotten as far as it did [with the Nationals] if it wasn’t appealing,” Greinke said in spring 2011. “The one thing I couldn’t get over was the fact that, here I was trying to get out of Kansas City because the team wasn’t good. Not saying [the Nationals] don’t have a chance, but I was trying to get to a team that was looking really good at the moment. And I believe [the Nationals] will be good eventually.”

The Nationals are good now, coming off a 98-win season powered by a rotation that, if Rizzo has his way, will only get better.