Sunday afternoon brought about a spare of bets on the former Chelsea and Manchester United boss.
It was enough to prompt Paddy Power to cut the odds from 66/1 to 14/1, meaning Mourinho is now among the favourites for the job.
A spokesperson said: “Jose Mourinho and Celtic may not seem like a natural partnership, but the Bhoys do have recent experience in coaches with humongous egos. And, actually, both parties have pretty strong links with Champions League success in Portugal.
“It could be viewed as an odd move for Mourinho but, having linked himself with the jobs at PSG and Bayern, Celtic would fit with apparent approach of targeting one-club leagues.”
Yet, the ex-Real Madrid manager was not the only person to see their odds slashed for the job.
Celtic legend Martin O'Neill went from 80/1 to 7/1 for a Parkead return.
Paddy Power have been forced to slash the odds on Jose Mourinho being the next permanent Celtic manager, from 66/1 to 14/1.
O'Neill is currently manager of Nottingham Forest and he has had previous with Mourinho. The pair faced each other in the 2003 Uefa Cup final, Porto defeating Celtic 3-2 in the extra-time in Seville.
Yet, current interim boss Neil Lennon remains favourite, although he is odds against (11/10) for the first time since taking over, after an uninspiring few weeks.