The 47-year-old, who was sacked by AC Milan last season, took over at the Serie A champions in the summer after Antonio Conte left to take charge of the national team.
He was previously linked with the Tottenham Hotspur job, and while that did not materialise, Allegri has admitted that he has grown fond of the Premier League following time spent in London earlier this year.
"What particularly struck me was how good their infrastructures are and the huge enthusiasm that the crowd has," he told BBC Sport
"I hope, in the future, to have the opportunity to coach in England.
"I was in London for two months when I was dismissed by AC Milan. I saw some games to try and better understand English football. It's different from the Italian football, it's more fascinating."
Allegri led Milan to the Serie A title in his first season in 2010-11, following a successful spell at Cagliari.