The Everton winger has been linked with a move back to the Bhoys in the January transfer window.
Celtic manager Ronny Deila recently told The Herald that wage demands of the 29-year-old pose a problem in any deal.
However, former Celtic striker Sutton believes that the Scottish Premiership giants need to recruit someone like McGeady in order to lift the supporters.
“I know McGeady has his faults but he is exactly the kind of player Celtic need right now,” the former Chelsea striker wrote in The Daily Record. “They are crying out for someone who can lift the supporters and shake them out of their boredom.
“Aiden can do that. He might not have the same burst of pace he had when he was a kid but he can still beat a man and produce a moment of magic.”
McGeady started his professional club career at Celtic and played for the Scottish giants until 2010. The winger then moved to Russian Premier League outfit Spartak Moscow and joined Everton in January 2014.
Things have not gone according to plan at the Toffees for the Republic of Ireland international, who is struggling for playing time at the moment.
McGeady has not made a single Premier League appearance for Everton so far this campaign, while last season he scored one goal and created 17 chances in 16 league games.
Celtic are not the only club linked with a move for the Everton winger in the January transfer window, though. According to The Times, Championship trio Middlesbrough, Derby County and Brighton & Hove want to sign McGeady this month.