The Juventus defender won three consecutive Serie A titles whilst working under Conte in Turin and is said to have a good relationship with the 46-year-old.
And with the Old Lady about to sign a superb replacement in Barcelona’s Dani Alves, The Sun claim Massimo Allegri will be prepared to part with the veteran right-back during the summer transfer window.
In fact, they believe Chelsea have already tabled a three-year contract and guaranteed first team football for next season, but the Switzerland international has requested time to consider their offer whilst simultaneously preparing for Euro 2016.
The 32-year-old struggled for form last season, finding just one assist from 30 Serie A appearances whilst averaging less than one interception per match.
But with his contract due to expire at the end of next season, the Blues could pick him up for a reasonable £12million this summer.