However, Tigers chairman Adam Pearson says that it will cost Villa if they want Taylor, as he still has two years remaining on his contract.
He said: "If a Premiership club does come in for the manager then there is something in his contract - an understanding - which enables him to talk to them. There is also a set figure of compensation that the club would need to pay to release him.
"But to be honest I have not heard anything about this and I have certainly not had a call from Aston Villa asking for permission to speak with Peter. We would expect this sort of rumour about a manager like Peter who has a good reputation within the game."
Former City manager Brian Little has also confirmed his interest in a return to Villa Park.
Meanwhile, Pearson has revealed City are set to sign full-backs Andy Dawson and John McDermott in the summer, along with Tranmere midfielder Jason Price.