ATLANTA -- The Nationals’ biggest priority ahead of the July 31 Trade Deadline is no secret. Their bullpen, which began Saturday with a 5.97 ERA, the second worst in the Majors, has been their most pressing need all season, one that threatens to derail their postseason goals if they fail to address it.

Nationals general manger Mike Rizzo is not just considering the rest of this season when he thinks of ways to improve his bullpen, however, telling MLB Network Radio on Friday that he prefers relievers with years on their contract beyond 2019.

Washington has expressed interest in a few relievers who match that description, checking in on Tigers closer Shane Greene, Giants right-hander Sam Dyson and Royals left-hander Jake Diekman, a source confirmed to MLB.com, as Ken Rosenthal of the Athletic first reported. The Tigers reportedly have a high asking price for Greene and are believed to have asked for shortstop Carter Kieboom, the Nats’ top prospect and the No. 20 overall prospect per MLB Pipeline, in return but Washington has balked at including Kieboom in any deal so far, per a source.

“When you’re giving away the assets that you have to give away at the Trade Deadline you kind of like to get a little bit of control in the players that you acquire,” Rizzo said on Friday afternoon. “I think that we pretty much with our play have made it clear that we’re going to acquire some talent to help us win this year and beyond. And we can do that in several different categories, and we’ll see what leads us to the best outcome and helps this team take the next step and really [plants] us as one of the playoff type of teams in the National League.”

How aggressive the Nationals will be ahead of the Trade Deadline -- July 31 is the only deadline this year and there will be no August trades -- remains to be seen. They remain approximately $6 million under the competitive balance tax, according to Cot’s Baseball Contracts. The Nats began the season reluctant to surpass that mark.

But since May 24, the Nationals have been the best team in baseball, boasting a record of 32-14 to revive what once looked like a lost season. Their bullpen during this stretch has been serviceable, and they have received contributions from a few of the veteran relievers they acquired from the waiver wire, including Fernando Rodney and Javy Guerra. But a more stable and reliable reliever to pair with Sean Doolittle could catapult them into the top tier of the NL.

Greene, 30, has been lights-out for the Tigers this year, with a 1.03 ERA and 22 saves in 35 games. He will be arbitration eligible in 2020 and cannot become a free agent until ’21.

Dyson, 31, has closing experience with the Giants and Rangers and has posted a 2.68 ERA in 45 games with San Francisco this season. The Giants have been one of the hottest teams in baseball recently, which has made their moves at the Deadline a lot less clear, but Dyson is also not eligible for free agency until ’21.

Diekman, 32, does not have as much time remaining on his contract as the others, but he does have a mutual option for 2020. He owns a 4.89 ERA in 45 games for Kansas City this year, but with a respectable 3.61 FIP and strikeout-to-walk ratio of 57-to-23.

“Our priority is going to be on pitching,” Rizzo said. “Probably bullpen arms that can give us some veteran leadership and possibly shorten the game up for our starting rotation.”