Milner has missed City's last four games through a combination of suspension and a hamstring injury. The England international incurred a one-match ban for his sending off in the Barclays Premier League win at West Brom on October 20 and then pulled up in the warm-up at West Ham a fortnight later.
Speaking in an interview published on the club's website, www.mcfc.co.uk, Milner said: "I've been progressing well and I'm back training so I'm hoping to be available for Villa."
He added: "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 okay, 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 10 days or so before I started light training again and now everything feels fine."
Milner, 26, joined City in a reported £26million deal which saw Stephen Ireland move in the opposite direction in the summer of 2010. He has since been a solid and consistent member of the City midfield pack even if manager Roberto Mancini uses him off the bench as much as starting him.
The former Leeds prodigy played a key role in last season's title success and feels his effort is much appreciated by supporters.
He said: "The fans have been brilliant since day one. I can't deny it's really nice and gives you a massive lift when you hear the best part of 47,000 singing your name like they did against Sunderland.
"I just want to go out and play as well as I can for City and our supporters and hopefully keep the trophies coming."