The midfielder, who is set to leave the Red Devils on a free transfer this summer, has not played for the 20-time English champions since picking up a calf problem against Liverpool in the middle of April.
Pogba has stepped up his injury recovery in recent weeks, though, and there have been suggestions that he could be fit for the contest at Selhurst Park.
Speaking during his pre-match press conference on Friday, interim head coach Ralf Rangnick refused to reveal whether the France international would be available for selection against Patrick Vieira's side.
However, according to ESPN, Pogba has reservations about playing against Palace, as he fears that he could be targeted by his own club's supporters.
The World Cup winner now has a strained relationship with the Man United fans, and he was booed at Old Trafford at the end of the 3-2 win over Norwich City last month.
The report claims that Pogba's fears over a negative reception at Selhurst Park could lead to him refusing to play in what would be his final match for the club.
The midfielder has made 27 appearances for Man United during the 2021-22 campaign, contributing one goal and nine assists in the process, but as mentioned, he has not been seen in a Red Devils shirt since limping off in the early stages of the 4-0 loss at Liverpool on April 19.
Pogba also missed a chunk of football earlier this season with a hamstring problem that he picked up while representing his country over the international break.
The Frenchman only made seven appearances for Man United in his first spell at the club, which ended with him moving to Juventus on a free transfer, but he has played 226 times for the club since returning in a big-money transfer in August 2016.
The midfielder will allegedly have to take a large wage cut to secure a return to the Old Lady this summer, but PSG are believed to be prepared to meet his demands.
Rangnick will manage Man United for the final time this weekend before stepping aside for Erik ten Hag, and the German will be bidding to lead the Red Devils to a top-six finish, which would see them qualify for the group stage of the 2022-23 Europa League.
The 20-time English champions are currently two points clear of seventh-placed West Ham United, who will end their season with a trip to Brighton & Hove Albion.
Palace, meanwhile, will enter Sunday's contest off the back of a 3-2 defeat at Everton on Thursday night.