Reports yesterday claimed Alex McLeish was preparing an £8 million (€9m) bid for the Bhoys’ star player, who has been on the Birmingham boss’ wishlist for some time.
But Mowbray, who this week allowed Gary Caldwell, Barry Robson, Chris Killen and Willo Flood to leave Parkhead, insisted there was no chance of winger McGeady following them out of the door.
“Aiden’s a very important player for our club in what we’re trying to build here,” said Mowbray.
“There’s no interest whatsoever in listening to bids.
“Other clubs would be wasting their energy picking the phone up.”
Mowbray sees McGeady as crucial to Celtic’s hopes of wresting the SPL title from Rangers.
“I wouldn’t sit here and say one player makes the difference,” he said.
“But what Aiden McGeady brings is that X-factor for us really, the ability in the Scottish game – where we do play against teams with a lot of men behind the ball – to eliminate individuals, to go past packed defences, to beat two and three men.
“Our financial situation is we don’t need to accept bids for players that we don’t want to sell.”
Mowbray’s stance will be welcomed by supporters concerned over the loss of Caldwell and Robson to Wigan and Middlesbrough, respectively.
Caldwell’s departure was inevitable after talks over extending a contract, which expired in the summer, broke down.
Robson still had 18 months to run on his existing deal and appeared to be a key component of Mowbray’s squad.
“Barry had done very, very well for us over the last month,” the Celtic boss said.
“He’s a wonderful personality, he’s great to work with on the training ground.
“Contractually, I think the deal that Barry got at Middlesbrough suits Barry Robson. The club are happy with the deal they got also.
“If there’s a frustration amongst the fans then, ultimately, myself as a manager will be judged on the team as we move on.
“Players do leave football clubs; new players come in and the team will progress.
“I’ve stated from day one that I’ll try to build a team, try to mould a team over a period of time.”