The striker picked up the problem while away on international duty with England and consequently missed the league win at the Stadium of Light and the FA Cup defeat at Stamford Bridge.
Sir Alex said Rooney felt the injury again in training on Sunday, but hoped he would be available for the clash with Manchester City at Old Trafford on 8 April.
Jonny Evans, meanwhile, missed the 1-0 loss at Chelsea because of a hamstring strain picked up in Saturday's victory over the Black Cats.
The Northern Ireland international replaced the injured Rafael in the first half at Sunderland and although he completed the remainder of the game, Sir Alex said afterwards that Evans had played through the pain barrier for much of the second period.
