Smalling was replaced by Michael Carrick two minutes before the break after the defender complained of sickness.
But according to the Mirror, sources close to Smalling say he will be fit to face to Villans at Old Trafford.
Louis van Gaal's side will be aiming for the victory over Tim Sherwood's side as their continue their hunt for a Champions League spot.
The Red Devils go into the game sitting in fourth, but a win could see them leapfrog Arsenal into third if the Gunners fail to beat Liverpool.
Smalling has recently praised Van Gaal for keeping faith in the England international.
"The manager has shown a lot of faith in me and especially in these last couple of months," he said.
"I have stayed fit. The manager has chosen me and I am enjoying my football."