Italian Sky Sports journalist Gianluca Di Marzio has claimed Celtic's search for a new manager has targeted Mourinho with the famous club believed to have offered the 56-year-old the job.
The Hoops have been without a full time manager since February when Brendan Rogers left the Scottish champions to take over at Leicester City.
Celtic appointed former coach Neil Lennon in the interim as the club chased a unprecedented treble treble with the search for a permanent boss delayed until the off-season.
Celtic would offer Mourinho a perfect chance to add to his already long list of title wins across Europe while also offering the Portuguese boss the chance to manage in the Champions League once again.
Tom Rogic has been an integral part of Celtic's success and it would be interesting to see how, or if, Mourinho would utilise him.
The same applies for Socceroos rising star Daniel Arzani who returns to Celtic for the second year of a two-year loan deal next season after a long stint on the sidelines with a knee injury.
Although Mourinho is thought to be holding out for an offer from PSG should they sack Thomas Tuchel, a move to Glasgow could be on the cards if his preferred job in the City of Lights doesn't eventuate.
The former Chelsea, Real Madrid, Porto and Inter Milan boss has also been linked with a move back to Serie A to coach Roma.
