Pogba missed France's Nations League double-header last week after testing positive for coronavirus .
Manager Ole Gunnar Solskjaer said Pogba has returned to training but is not certain to feature against Palace.
"Paul's lost out on a few sessions because of the virus," Solskjaer told MUTV.
"He is quick to get fit and hopefully he'll be ready for next weekend. I am not 100% sure though."
Pogba was forced to withdraw from France’s squad for this month’s Nations League matches after testing positive for the novel coronavirus.
The 27-year-old has recuperated and is working on his fitness but Solskjaer said he needs more time.
“Paul’s had a couple of training sessions so he’s lost out on a few sessions because of the virus, of course,” Solskjaer told MUTV.
Pogba struggled with an ankle injury last season but returned after the league’s restart in June to help United finish third in the table.
They do not play on the opening weekend of the new season due to their participation in the 2019-20 Europa League knockout phase in August and will kick off against Palace on Sept. 19