Mourinho is widely expected to be confirmed as interim manager Rafael Benitez's replacement at Stamford Bridge after Real Madrid on Monday night announced the 50-year-old was leaving the Spanish giants at the end of the season.
Mourinho led Chelsea to five major domestic trophies, including back-to-back Premier League titles, in three seasons in charge of the Blues before leaving the club in 2007.
Since then, Mourinho has gone on to have a hugely successful spell in charge of Inter Milan - including guiding the Italian side to an unprecedented treble in 2010 - before moving to Madrid, where he won three titles during a mixed three-year spell.
With all that experience in mind, West Ham manager 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."
England manager Roy Hodgson also believes Mourinho will be welcomed back to the Premier League - not least by the media.
Mourinho has made headlines throughout his coaching career, both because of the success of his teams on the pitch and also some of his outspoken comments and controversies off it.
Hodgson, who was coaching abroad while Mourinho was in charge of Chelsea, told Sky Sports News: "He's very popular and did a wonderful job last time he was here and I'm sure that the people, especially the media people, will be very pleased to see him and whichever club happens to get him as a manger will be very glad to have him there."