The Hoops were dealt with a shocking blow after Brendan Rodgers sought an exit to the Premier League club Leicester City.
Neil Lennon was appointed as the manager on a makeshift basis and has enjoyed a great run since taking the charge.
The Portuguese gaffer recently managed Manchester United and was sacked by the club following a poor start to the campaign. Ole Gunner Soslkjaer was appointed as the new manager of the Red Devils after an impressive spell as the caretaker boss.
Mourinho is regarded by many as one of the greatest managers of all time for his success in Europe.
The former Porto manager has won 25 major honours and he is best known for his spells at Chelsea and Inter Milan.
He has won two Champions League title with Inter Milan and Porto, and three Premier League title with the Blues.
Odds are in favour of Lennon
The Portuguese manager has been tipped to move to Italy and France.
Instead, Lennon, the former Hoops captain, is more likely to continue as the manager permanently, owing to his impressive results.
Lennon had his seventh win of the season against Kilmarnock and he is yet to face a defeat.
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The former Hibernian manager inspired the Bhoys to a dramatic Old Firm derby win and ensured a place in the Scottish Cup final.