The Irish striker has missed the last six games after picking up the knee injury after scoring the winner against Middlesbrough on December 5.
Martin Jol reported on Boxing Day: "Robbie has started to do some ball work, he's also done a lot of pool work with his knee so hopefully he'll be back in two, maybe three weeks time."
However, Mido was sidelined for the win against Villa with a slight groin injury sustained in training.
Martin added: "Mido was going to be on the bench if anything went wrong with Jermain Defoe or Dimitar Berbatov but we had a finishing session for the players who weren't involved at Newcastle and he got injured then."
Robbie Keane has started training with the ball again as he recovers from medial ligament damage.