The club has confirmed that Allegri will be departing at the end of the Serie A season.
Sarri would be open to a move back to his homeland after a difficult season at Chelsea.
Sarri remains unpopular at Stamford Bridge despite meeting expectations by delivering a third-place finish and a run to the Europa League final.
The newspaper claimed that the Bianconeri are also fans of Pochettino, who has led Tottenham to a top-four finish and the Champions League final this term.
