And sources close to the 22-year-old are optimistic he could look favourably on following Liam Ridgewell from Villa to Blues.
Bolton had a bid accepted on Monday for Cahill who has recently returned from a three-month loan spell with Sheffield United.
But that prompted City, who had originally hoped to sign the player on loan, to match their offer which comprises a £4million down payment plus another £1million in add ons.
Ridgewell has proved that switching from Villa to Blues will not be a problem in terms of winning over the fans and he was made captain when Damien Johnson was out injured.
And Ridgewell has assured Cahill that he can be assured of a similar welcome if he proves his worth and commitment to the cause.
Ridgewell said: "I'd like to see Gary join us. He just wants to play first team football. It would be good to link up with Gary again.
"People make a lot about the move between Villa and Birmingham but you just want to play football. You just want to play week in and week out.
"That's what I wanted and so does Gary now and I've got on well with the fans here."