With speculation continuing to link further clubs from England's top flight with the 23-year-old, Mowbray now feels the time is right to publicly dismiss any interest.
"Aiden's a very important player for our club and what we're trying to build here and there's no interest whatsoever of listening to bids," he told Sky Sports News.
"I think clubs would be wasting their energy even picking the phone up, such is our situation with Aiden at the moment."
McGeady is seen as the Bhoys' most lucrative asset in a squad struggling to perform under the former West Brom boss in his first season in charge.
But with five goals in 16 league starts, Mowbray was also keen to highlight the creative spark McGeady possesses - an essential ability in the Scottish Premier League he feels.
"What Aiden McGeady brings is that X-factor for us - the ability, in the Scottish game where we do play against teams with a lot of men behind the ball, to eliminate individuals, to beat two or three men as he so often does for this club to create space for somebody else to score a goal.
He added: "So, Aiden is a very important factor for us in our, hopefully, future success."
Celtic v Falkirk To Score in 90mins: McGeady, A. 6/4