The 26-year-old has been absent for City's last four games due to a one-match suspension for his red card against West Brom followed by a hamstring injury.
The England international pulled up during the warm-up before the West Ham game which would have been his first game back after his ban.
Milner told the club's official website: "I've been progressing well and I'm back training so I'm hoping to be available for Villa.
"My hamstring was a little tight before the game at West Ham and hadn't felt quite right in the days leading up to the game.
"I'd had some treatment because it happens from time to time - then you play and it's OK, but I went to do a sprint in the warm-up, it didn't feel right and I made the decision not to carry on which I think has been proved correct.
"If I'd have played, it would have probably gone during the game and I could have been out for a lot longer. As it was, it was just ten days or so before I started light training again and now everything feels fine."