Here, we look at some of the likely contenders.
The man known as the 'King of Kings' by an adoring Parkhead public is already the clear favourite to replace Neil Lennon as Celtic boss. Idolised after netting 242 goals in 315 games for the Hoops between 1997 and 2004 before departing for Barcelona, the Swede would win the instant backing of the club's huge support. Has managerial experience having bossed Landskrona and current club Falkenberg in his homeland but nothing that will prepare him for a return to Celtic.
The Aston Villa boss is another former Celtic player whose playing honours would certainly win him kudos from the Celtic faithful. He skippered the team which lost in the 2003 UEFA Cup final in Seville and has gone on to build-up a decent managerial record with stints in charge of Wycombe, Colchester and Norwich. However, he had faced difficulties in his efforts to transform Villa during his two-year stint in Birmingham and may fancy a return to 'Paradise'.
The Parkhead crowd value tradition and that may also open up the door for sacked Cardiff boss Mackay. Another to have worn the Hoops during his playing days, he has been out of work since his spectacular fall-out with Bluebirds owner Vincent Tan. The 42 year-old kept Watford in the Championship in his first managerial job before guiding Cardiff into the Premiership, so he can boast about a track record of success.
Yet another one-time Celtic recruit tipped with a return to Glasgow's East End. However, Moyes may see Scotland's top flight as too big a step down to take just a month after being axed by Manchester United. Lennon's departure is rumoured to have been sparked by the club's lack of financial might in the transfer market and that will hardly help convince the former Everton boss to return home after more than three decades south of the border.
You guessed it, another former Hoops player. But the Dundee United boss has made an encouraging start to life as a manager since hanging up his boots three years ago and makes for a decent outside bet. Sent Partick on their way to the Scottish Premiership last season but quit to take over at Tannadice before promotion was clinched. His enthusiastic young team may have lost out on the William Hill Scottish Cup at the weekend but they have enthralled supporters with their free-flowing football this term.