NEW YORK -- Mets right fielder Michael Conforto and second baseman Jeff McNeil have hamstring injuries that are likely to keep them out of action for another month.

"They're significant hamstring strains," general manager Zack Scott during Monday a lengthy recounting on the Mets' MASH unit, which currently has a major league-high 16 players on the injured list with right-hander Jordan Yamamoto set to join. "If I'm putting a timeframe on that, we're probably looking at late June."

Conforto and McNeil both got hurt on April 30.

Right-hander Carlos Carrasco, sidelined by a strained right hamstring, won't be ready to pitch for the Mets until late June or early July, Scott said. The six-week timetable from now is the same as the projection when Carrasco first got hurt on March 18.

When Carrasco was moved from the 10-day to the 60-day IL on May 9, Scott said there had not been a setback.

"Probably when I spoke before, the word 'setback' to me implied something more specific," Scott said. "So it's kind of semantics a little bit. So obviously, when we're backing off, like I said back then, what we've done, that probably falls under setback in a different way."

In addition, Yamamoto left Sunday's game at Miami with soreness in his pitching shoulder, was having an MRI on Monday and likely will go on the injured list Tuesday, when ace Jacob deGrom is ready to be activated following right side tightness that has sidelined him from May 9.

New York's shortage of players reached the point Monday that James McCann, the Mets' starting catcher, was set to make his first start at first base in his 994-game professional career.

"Definitely I am aware that adding some some additional talent is important, and we're going to try and do that," Scott said. "This time of year, what's typical is teams kind of are still waiting and seeing where they're at. It's pretty early.

Infielder-outfielder J.D. Davis, out since May 1 with a sprained left hand, will likely play at least three more rehab games, including one at first base, before returning. Davis went 2 for 11 with one home run since starting at Triple-A Syracuse on May 18.

First baseman Pete Alonso, sidelined by a sprained right hand since May 18, was to swing with two hands Monday and also will have at least one rehab appearance before returning, possibly next week.

Outfielder Brandon Nimmo has been out since May 2 with a bone bruise in his left index finger that has impacted a nerve.

"It's just something that's probably going to need some time and we've got to figure out where we can get to a tolerance where he can play," Scott said.

Right-hander Noah Syndergaard, coming back from Tommy John surgery on March 26 last year, is on track for a mid-June return after making his first minor league injury rehabilitation start. He pitched four scoreless innings for St. Lucie against Palm Beach last Wednesday.

Infielder Luis Guillorme, who hasn't played since April 25 due to a strained oblique muscle in his right side, could start a rehab assignment next week.

Right-hander Seth Lugo, working his way back from surgery to remove a bone spur from his pitching elbow, likely will be activated May 31, when he becomes eligible, or the following day. Lugo pitched a scoreless inning for St. Lucie on May 18 and allowed an unearned run in one inning for Syracuse on Friday.