Allegri has confirmed his departure from Juventus after winning Serie A five times in as many years and extending their reign of Italian titles to eight in a row.
Sarri is in their thoughts as an option in Turin but will not enjoy a clear run at the coveted job.
Juventus came up with an ambitious top tier of targets topped by Pep Guardiola, who has already confirmed he remains committed to Manchester City.
Tottenham manager Mauricio Pochettino is also much admired by the Italian giants and they like the idea of a return for Antonio Conte, who led them to a hat-trick of titles before Allegri took control.
Conte is thought to have an agreement to join Inter Milan at the end of the season. Pochettino has four more years on a contract at Spurs and Juventus are not keen to pay millions in compensation for their next coach.
There are others in the frame but Sarri has only one year on his deal in London and is thought to be interested in a return to his native Italy.
He has endured a difficult first year at Stamford Bridge, with some Chelsea fans turning against him, and was close to sack in mid-season.
Sarri did not endear himself to Chelsea officials when he criticised a post-season friendly in the United States which raised more than £3.1million for charities fighting anti-Semitism and other forms of discrimination.
He did not make further public comment while in Boston last week for the game against New England Revolution and was unable to attend a visit by 23 players to the city’s Holocaust Memorial because he was feeling unwell.