The 50-year-old has two years remaining on his current contract, but Allegri is reportedly being monitored by several English clubs.
According to Yahoo! Sport, the Italian coach is on the managerial shortlists of both Arsenal and Chelsea.
The report adds that Allegri is attracted by the thought of living and working in London, but would only move overseas if he has "a real chance to win".
Allegri's Juventus need a point against Roma on Sunday to wrap up their seventh consecutive Scudetto.