Mourinho is widely expected to be confirmed as interim manager Rafael Benitez's replacement at Stamford Bridge after Real Madrid 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."
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