PITTSBURGH -- Mets manager Mickey Callaway may be coming closer to the idea of a flexible -- yet still high-leverage -- role for current closer Edwin Díaz.

Diaz has given up runs in his past four appearances, including three home runs, and he’s posted a career-worst 5.44 ERA after the Mets acquired him in a package deal with the Mariners this offseason.

A month ago, when Diaz allowed four runs in a July 5 outing against the Phillies, Callaway said, “If somebody steps up and is getting the job done better in that role, then we would consider it.” That push is coming from setup man Seth Lugo, July’s National League Reliever of the Month, who hasn’t allowed a run in more than a month’s time.

Callaway has taken notice, and he’s open to considering Lugo for the closer’s spot depending on the situation.

“We think that moving forward, it’s just something that we’re going to do whatever we can to win a game, and I don’t think we can lock ourselves in to one thing,” Callaway said on Sunday.

Callaway and Diaz hadn’t spoken with one another about the possibility yet, according to Diaz, but the manager said Diaz “understands that he’s going to go out there when his name is called.”

For his part, Diaz understands the situation his results this year put him in. He’s working on his mechanics, trying to find ways to cut his 2.09 HR/9 rate, and he still believes his stuff can play in a tight game.

“I would love to be the closer,” Diaz said through a translator. “I feel like I’ve proven [it] and my numbers have said I’m the closer of the team. If I get the opportunity, I’d want to do the same thing.”

If he were to move into a different role, in the short term or long term, Diaz said it won’t change his mentality, the one that earned him a 2018 American League Reliever of the Year Award with the Mariners.

“That’s not going to take my confidence away,” he said. “All I want is the opportunity to keep pitching and keep helping the team win.”

Lugo has one save this year -- July 26, against the Pirates -- though he was charged with three blown saves in June as the seventh- and eighth-inning guy. But after beginning the year by allowing 12 runs in 17 2/3 innings, he’s turned a corner and recorded a 2.00 ERA over his past 30 games, including his current 13-game scoreless streak.

“I think that we’re going to play the situation as we see fit,” Callaway said.

Rhame to IL, Hart recalled

Donnie Hart, whom the Mets claimed off waivers on Saturday from the Brewers, has been added to the Mets’ roster after Jacob Rhame was placed on the 10-day injured list with right elbow discomfort.

Rhame pitched 1 1/3 scoreless innings in Saturday’s victory over the Pirates after being recalled earlier that day. He’s pitched in five games this season, allowing four runs (three earned).

Hart, 28, tossed four scoreless appearances for the Brewers across April and May. He owns a career 3.17 ERA in 97 games.