Villa suspended the midfielder while they carried out an internal inquiry after he was arrested on suspicion of drink driving on October 23.
Villa boss McLeish said: "He's feeling it a bit - he wouldn't be human if he wasn't. You can't expect somebody to be singing and dancing as if nothing's happened. We'll see how the week unfolds."
Bannan's return to training coincided with reformed alcoholic Alex Rae's visit to Villa - the former Wolves midfielder talks to youngsters to warn them about the dangers of drinking.