The England defender played over an hour for the club's Under-21 side on Monday night and could be involved at Palace on Saturday.
Phil Jones says he is ready to return for Manchester United and help them clinch a top-four spot.
Jones played 62 minutes for the reserves against Southampton on Monday night, after being an unused sub in United's 1-0 defeat at home to West Brom on Saturday.
The England defender has missed United's last three games, but has made a full recovery from the ankle injury that sidelined him and is ready to play a part in the final three games of the season.
"I'm happy to play in the Under-21s and get some fitness," said Jones.
"The lads did well. I feel I'm ready to go again and hopefully I can make the squad on Saturday.
"Hopefully, I'll recover on Tuesday, then train on Wednesday and Thursday, and see how it goes. I'll take it from there.
"[As a team], we've got a long way to go, as there are still three games coming up, three massive games, and we've got to approach it in the right way.
"I'm sure we can do that and cement that top-four finish."