Chelsea midfielder Cesc Fabregas has thanked Conte on social media and wished him “luck for the future”.
Ex-Napoli manager Maurizio Sarri is expected to take over from Conte, who took pre-season training this week.
The club have refused to comment on the status of the 48-year-old, who won the Premier League title in his first season and the FA Cup in May.
Should Sarri be appointed, he would be Chelsea’s ninth full-time manager since Roman Abramovich bought the club in 2003.
Conte’s mark of 30 league wins in the 2016-17 campaign was a record until Manchester City produced 32 in 2017-18.In all he won 69 and drew 20 of his 106 games in charge of the club.