The Portuguese left Stamford Bridge having won five trophies in three seasons, and is set to return to the club in the next two weeks after stints managing Inter and Real Madrid.
|1/20||Jose Mourinho is 1/20 with Paddy Power to be in charge for Chelsea's first game of the season
"I suppose it depends on whether he can recapture what he did when he first moved to Chelsea," Allardyce told Sky Sports.
"Looking at his experience since those days, he should be better than 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.
"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."
With Mourinho set for a return to Chelsea, Allardyce says he and the rest of the Premier League will be happy to see the former Porto boss working in the capital again.
"I think it will be great to have him back," he added.
"He had a very good spell last time. I know it didn't finish so well in the end at Chelsea with [owner] Roman Abramovich but obviously they've repaired that damage and it sounds like he's looking forward to coming back to England.
"We'll be glad to see him and obviously pit our wits against him again."