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Allegri was appointed as Bianconeri boss in May after Andrea Pirio was relieved of his duties following a poor season, ending with the club only fourth in Serie A.
The experienced Allegri led the Turin giants to five consecutive Serie A titles, four Coppa Italia triumphs and two Champions League finals during his previous tenure.
Allegri, 53, on Tuesday revealed he could have taken over at Madrid before Carlo Ancelotti was appointed as head coach.
Read More I have to thank Real Madrid and the president for the opportunity he gave me [to coach Real Madrid]. Then I thought about it and chose Juventus, Allegri said during his presentation news conference.