Both Allegri and his predecessor at Juventus, Italy coach Antonio Conte, have been linked with the Chelsea manager's job currently being filled on a caretaker basis by Dutchman Guus Hiddink following the sacking of Jose Mourinho.
Allegri's contract in Turin expires in 2017 and he says he is "happy where I am".
But Giovanni Galeone, who coached Allegri at several clubs during his playing career and is described as his mentor, believes the Juve boss will capitulate and quit the Turin giants to take over at Chelsea in time for next season.
"If I was Allegri, I would walk to Chelsea and I think he will end up there at the end of the season," Galeone said in an interview with Radio Radio.
Allegri took over from Conte in time for the start of last season and led the Bianconeri to a fourth consecutive Serie A title, their first league and Cup double in 20 years and their first Champions League final appearance since 2003.
Juve were outclassed 3-1 by Barcelona in the Berlin final but despite the recent demise of teams in cash-strapped Serie A, Allegri helped return the Turin giants to the upper echelons of Europe's elite operators.
Juve underwent several key personnel changes in the summer following the departures of Andrea Pirlo (New York City FC), Carlos Tevez (Boca Juniors) and Arturo Vidal (Bayern Munich).
After a disastrous start to the campaign, Juve are now only two points behind leaders Napoli ahead of the sides' top-of-the-table clash next Saturday in Turin.
Juventus are keen to hang on to Allegri and the prospect of his departure has already prompted Juventus CEO Beppe Marotta to warn: "Allegri is already at a top club. He should think twice before leaving Juventus."
Galeone believes the 48-year-old Allegri, who also led AC Milan to their last league title in 2011, has the man-management skills and tactical nous to get the best out of the players under his command.
And he is sure Allegri, who has been taking English lessons in recent years, will ultimately succeed Mourinho.
"He's performing miracles (at Juventus) considering that during the summer he didn't get any of the players he'd asked for," added Galeone.
"Max has reinvented Paulo Dybala as a top playmaker. He's one of the best five coaches in the world.
"I think he will go to Chelsea because the offer is really fantastic."