SAN FRANCISCO — Zack Wheeler may throw a full bullpen session as early as Sunday, possibly the final step before he is considered for activation from the injury list.

The right-hander has not pitched in two weeks because of an impingement in his right shoulder. If the Mets are going to deal Wheeler by the July 31 trade deadline, he will need to get on the mound for at least one start this month to show he is healthy. Wheeler could conceivably pitch twice before the trade deadline if he is slotted into the rotation by Thursday.

A club source indicated there is belief within the organization that despite the injury setback, the Mets can still get a solid return for Wheeler — who is eligible for free agency after the season.

Wheeler, who is 6-6 with a 4.69 ERA in 19 starts this season, has been playing catch and throwing from the slope of a bullpen mound.

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Luis Avilan is emerging as a trusted option in the Mets’ bullpen since his return from the IL this month. The veteran lefty, who did not pitch Saturday, is without a run allowed in five appearances since his return. And lately manager Mickey Callaway has been unafraid to use him in tie games or to protect a lead.

“I think he is totally healthy and he’s getting in there more often,” Callaway said. “The velocity on his fastball is good and his changeup is good. I think it’s just getting into the season.”

Callaway said the emergence of Avilan and fellow lefty Justin Wilson has helped lessen the workload on Jeurys Familia and Robert Gsellman, in particular.

Wilson Ramos was behind the plate for Saturday’s matinee following a night game because Callaway said he wanted the veteran catcher’s bat in the lineup. Ramos was 1-for-4 with a strikeout.

“He wants to catch as much as possible and when we talked to him after the game [Friday] he said, ‘Heck, yes, I want to catch tomorrow,’ ” Callaway said. “We want him in there and we need his offense obviously, runs have been hard to come by, so get him out there and let him swing the bat.”