Lambert is in negotiations with Villa while the Birmingham club work on a compensation package with the 42-year-old's current club Norwich.
Scotland international Bannan, 22, believes Lambert's managerial history would make him an ideal candidate. "If it is him then that will be good," Bannan told Sky Sports News.
"He has done very well with Norwich and the clubs he was at before then. He has a good record up until now so hopefully if it is Lambert he can be as success with us as he has with his previous teams."
Villa finished last season 16th in the Barclays Premier League as Alex McLeish was sacked after just one season, but Bannan is hoping Lambert's potential appointment would inject fresh impetus into the club.
He said: "Obviously last season wasn't the best for a team as big as us.
"We should have been way higher up the league and I think they see Lambert as an up-and-coming manager that is doing really well, so it is going to be a massive lift for everyone, the fans and the players as well.
"It is a fresh start for everyone again and hopefully in pre-season everyone is going to have a chance to prove their worth to the club."