The midfielder, Scotland's player of the year in 2008, has scored five goals this season and is a huge fans' favourite.
"I wouldn't sit here and say one player makes the difference," added Mowbray in praise of McGeady.
"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."
Celtic have moved Gary Caldwell, Barry Robson, Chris Killen and Willo Flood on this week and recruited Dutch defender Jos Hooiveld, who has won titles in Finland and Sweden.
And Mowbray revealed he was close to making further additions to his squad this month.
Hooiveld ready to fight for place
"We're pretty well down the line with a few things," he said ahead of Saturday's game with Falkirk.
"The life of a football manager throughout January is an interesting one, of very long hours and lots of conversations.
"You think you're very close to doing a deal and then you're not.
"Every club you talk to wants £10m for every player you ask about."
Hooiveld has not played since AIK Stockholm's campaign finished in November and will take two weeks to build up his match fitness.
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