SAN FRANCISCO — Zack Wheeler has taken the first steps in what the Mets hope will be a fast return from the injured list.

On Thursday, the right-hander played catch for a second straight day and reported feeling OK as he battles an “impingement” in his right shoulder. The earliest Wheeler can pitch again is Tuesday, but there hasn’t been an indication yet whether he will be ready by then. Wheeler would first have to throw bullpen session.

The calendar remains important to the Mets if they want to deal Wheeler — an impending free agent — before the July 31 trade deadline. If he were to return by next Thursday, he could conceivably pitch twice to showcase his physical readiness.

“Continuing to play catch will dictate a lot of what goes on next,” manager Mickey Callaway said before the Mets lost, 3-2, in 16 innings. “We’ll just kind of feel him out day-to-day and see where we’re at.”

Walker Lockett will take Wheeler’s spot in the rotation and pitch Saturday against the Giants. The right-hander is 0-1 with an 11.74 ERA in two starts for the Mets this season. In seven appearances for Syracuse, he is 1-2 with a 3.92 ERA after opening the season on the injured list.

Pete Alonso remained in the No. 3 spot in the lineup, even with Michael Conforto on the bench against Giants lefty Madison Bumgarner. Alonso had been batting second until Callaway moved Conforto into that spot after the All-Star break.

“Right now we’re trying to get some guys on, so when [Alonso] hits one 474 feet, maybe it’s multi-runs,” Callaway said, referring to Alonso’s blast in Minnesota a day earlier. “I kind of want to get Pete comfortable in that spot.”

J.D. Davis batted in the No. 2 hole in Conforto’s place.

Brandon Nimmo has begun participating in baseball activities after a month-long shutdown for a bulging disc in his neck. But Nimmo will have to ramp up into baseball shape before beginning a minor league rehab assignment within the next few weeks.

Jacob Rhame had his suspension reduced to one game upon appeal for throwing behind the Phillies’ Rhys Hoskins in April. The reliever served the suspension Thursday. Rhame had initially been suspended two games, but was optioned to Triple-A Syracuse before he could serve or appeal it. He returned to the Mets this week.