The Blues are in the market for a new boss, with Guus Hiddink’s interim tenure set to finish at the end of the season.
And Allegri has been touted as a potential replacement for the outgoing Dutchman, who stretched his unbeaten streak since returning to Stamford Bridge to 10 matches with the late draw against Manchester United on Sunday.
The Italian guided Juventus to a league and cup double last season, while also leading the Bianconeri to the Champions League final.
In pictures – Chelsea 1-1 Manchester United:
Chelsea owner Roman Abramovich has the financial muscle to make Allegri one of the best paid managers in world football, but Juventus director Beppe Marotta has issued the Russian with a hands-off warning.
“We have a great rapport with Allegri,” Marotta said. “Now the crucial moment of the season is coming up, so we should focus on that.
“In any case, contracts are not as important as the rapport between people. With Allegri the conditions are all there to continue.
“The team is doing well and improving a great deal.”