Mourinho's expected move back to Chelsea looks even more likely after Real Madrid confirmed he will leave the Bernabeu at the end of the season.
Allardyce locked horns with Mourinho during his last spell at Stamford Bridge and admits he would look forward to more touchline battles with his old managerial foe.
"I think it will be great to have him back," Allardyce told Sky Sports News. "He had a very good spell last time. I know it didn't finish so well in the end at Chelsea with Roman Abramovich.
"Obviously they have repaired the damage and he comes back to apply his talents in the Premier League. It sounds like he is looking forward to coming back to England.
"We'll be glad to see him and obviously pit our wits against him as well."
Mourinho failed to land any silverware during his last season in charge with Real Madrid, but he guided the club to the La Liga title in the previous campaign and secured the Champions League title during his spell at Inter Milan.
Allardyce does not think the 'Special One' has lost any of his talents and expects him to be a more dangerous adversary if he does take charge of the Blues again.
"I suppose it depends on whether he can recapture what he did when he first moved to Chelsea," he said.
"I think, looking at his experience since those days, he should be better than what he was when he left. I think that his spells in Italy and Spain, he will have matured and learnt a lot from that time.
"I suppose when he comes back to Chelsea, he'll use that experience and probably try to be better than when he left."