Wheeler threw from 90 feet on Thursday and has thrown from as far as 120 feet. Alderson said that the 26-year-old right-hander is slated to throw on a slope in the next couple of days, but also added that it is "unlikely" that he is back with the Mets in the next 30 days.
"He's had a couple of minor setbacks," Alderson said. "Nothing serious, but serious enough so that projecting any sort of return at this point is a little bit speculative."
Matt Harvey was placed on the 15-day disabled list on Wednesday with right shoulder discomfort and is currently weighing his options between season-ending surgery or a nerve-block injection to treat "symptoms consistent with thoracic outlet syndrome."
• Alderson: Harvey considering season-ending surgery
Wheeler's original timetable would have allowed the Mets to slot him comfortably into Harvey's vacated rotation spot, but instead New York will turn to right-hander Logan Verrett, who will oppose the Nationals' Max Scherzer on Saturday at Citi Field.
"We thought this week he would be doing his final start before joining us after the [All-Star] break," Collins said. "When we went into Spring Training, we looked at what a dynamic rotation this was going to be, and then when we got Zack back it was going to be even better. Now we don't know when he is coming back and most likely we may not have Harvey for a while, so it's been tough."
Alderson said that the club will keep an eye on Wheeler to make sure he does not put too much pressure on himself to hurry back and fill the void left by Harvey's injury.
"There might be a little bit of concern, but we just need to supervise what's happening," Alderson said of Wheeler. "He's been pretty good in terms of feedback as to how he feels, so I'm not overly concerned about that."
Wheeler underwent Tommy John surgery on March 25, 2015. In his first two seasons with the Mets in 2013-14, he went 18-16 with a 3.50 ERA, posting a 9-4 record with a 2.93 ERA in his final 18 outings.
Troy Provost-Heron is a reporter for MLB.com based in New York. This story was not subject to the approval of Major League Baseball or its clubs.