Pogba has missed the Red Devils' last two matches following the death of his father, who lost his battle with illness last week at the age of 79.
Mourinho was eager to get the France international back involved prior to the crucial Europa League final with Ajax next Wednesday, and he has been given a boost as his record signing is available for the visit of Palace.
"Paul is fine. He's a strong guy, has a strong mentality. He needs to play on Sunday," the Portuguese told reporters. "Chris Smalling has a small problem for Sunday; he will be fine for Wednesday."
Mourinho also confirmed that skipper Wayne Rooney will likely be rested and could therefore turn to some of his Under-23s players for the final league game of the season.
"To play so many kids at the same time, honestly, I don't think is good. I think they really need my support, Nicky Butt's and supporters to understand difficult job they have. It'll not be easy for them," he said.