Mauricio Pochettino and Massimiliano Allegri are also said to be in the running for the job but the Blues have accepted that Pep Guardiola will join Manchester City
Chelsea want to make Italy coach Antonio Conte their next permanent manager, according to the Daily Mail.
The former Juventus boss is reportedly set for talks with the Blues between the end of the club season and Euro 2016, where he is likely to bring to an end a two-year spell in charge of his country.
Conte won three Serie A titles in Turin and is said to be taking English lessons in preparation for a job in the Premier League.
Tottenham coach Mauricio Pochettino and Massimiliano Allegri, Conte's successor at Juventus, are also in the running but Roman Abramovich has accepted that Pep Guardiola will join Manchester City.