Allardyce feels Mourinho should be even better than in his previous stint in west London.
He told Sky Sports News: "I suppose it depends on whether he can recapture what he did when he first moved to Chelsea. Looking at his experience since those days he should be better than what he was when he left.
"I think that with his spell in Italy and his spell in Spain he will have matured and learnt an awful lot from that time and I suppose when he comes back to Chelsea he'll use that experience and probably try to be better than he was before he left."
If Mourinho does return, Allardyce for one is looking forward to locking horns with the Portuguese.
He added: "I think it will be great to have him back.
"He had a very good spell last time, I know it didn't finish so well in the end at Chelsea with Roman Abramovich but obviously they've repaired that damage and he'll come back to ply his talents in the Premier League and it sounds like he's looking forward to coming back to England.
"So we'll be glad to see him and obviously pit our wits against him again."