New York Mets starting pitcher Zack Wheeler looks on from...

New York Mets starting pitcher Zack Wheeler looks on from the mound against the Philadelphia Phillies during the first inning of an MLB baseball game at Citi Field on Sunday, July 7, 2019. Credit: Kathleen Malone-Van Dyke

SAN FRANCISCO — Zack Wheeler graduated to what manager Mickey Callaway called “glorified catch” on Friday, 13 throws from a mound at Oracle Park, another small step forward in his recovery from a right shoulder impingement. Wheeler also played catch out to 120 feet.

Callaway said the righthander will “absolutely” need to a throw a full bullpen session before returning from the injured list. The Mets don’t know when that will be, but have Jason Vargas, Noah Syndergaard and Jacob deGrom in their tentative rotation for the Padres series Tuesday-Thursday.

Every day matters for Wheeler and the Mets, who have until the July 31 trade deadline to deal the pending free agent. Wheeler has battled injuries for years but has been healthy and reliable this season and last. Him returning and showing he is healthy would aid the Mets’ efforts.

A looming question for player and team: Will Wheeler need a rehab assignment? Of the other four Mets starters to make brief stays on the IL, two made a minor-league start before returning. DeGrom (12 days between major-league starts) and Steven Matz (15 days) came right back to the majors. Syndergaard (15 days) and Vargas (20 days) each made one rehab start.

Wheeler’s most recent game was July 7.

What goes into that decision?

“You watch their catch game, you watch their bullpen, you talk to them, see their comfortability level with going out there,” Callaway said. “Do you feel good? Do you feel like you’re going to throw strikes? Do you feel like you can attack? And go from there.

“My guess is his ability to throw strikes [is a point in Wheeler’s non-rehab favor]. When the time comes, we’ll obviously know the timeframe at that point and make a decision.”

Roster rejiggering

Needing fresh arms after their 16-inning loss to the Giants on Thursday, the Mets called up Tyler Bashlor and Stephen Nogosek from Triple-A Syracuse. Chris Mazza and Luis Guillorme were optioned to Syracuse. Also rested was Jacob Rhame, who was unavailable Wednesday as he served a one-game suspension.

Bashlor has a 2.89 ERA (three earned runs in 9 1/3 innings) the past month. Nogosek has thrown seven scoreless innings since being sent back to the minors early this month.

Callaway said both have been doing “all of the things we stressed to them when we sent them down.”

“The things we need to see out of our bullpen pieces to have success — getting ahead, controlling the count, throwing two out of the first three pitches for strikes and making guys hit the ball early,” Callaway said. “Don’t let them see seven pitches and track six of them and hit the seventh one really hard.”

Tough luck for Mazza

Sometimes, baseball is cruel.

Mazza, 29, is a Bay Area native — born on Oct. 17, 1989, the day an earthquake stopped the Giants-A’s World Series — and was a career minor-leaguer until getting called up by the Mets last month. He was with the team again to open the second half, including this series in San Francisco, and spent time pregame Thursday chatting with visitors on the field.

A starter by trade, Mazza ended up pitching the 15th and 16th innings Thursday, a day after pitching two frames in Minnesota. The Giants came back to turn what would have been Mazza’s first big-league win into his first big-league loss.

Extra bases

After a long game Thursday and before a quick turnaround/day game Saturday, Callaway rested Todd Frazier on Friday. He indicated other regulars would do so Saturday. Will Pete Alonso be one of them? “We’ll see,” Callaway said with a smile. “I hope not.” … The Mets bullpen had a 2.16 ERA — good for third in the majors — in six games to begin the second half entering play Friday.

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