The Times says Conte is considering quitting as head coach at the end of the season.
He has signalled his interest in leaving Chelsea due to his long-term unhappiness with the club’s board.
The Italian was close to resigning last term before agreeing a contract renewal that did not extend the length of his deal.
Conte told Italian radio last week that he “will be home before long”.
He added: “I miss Italy, that’s beyond doubt, so once I have had some important and life-changing experiences, I will be back.”