The Italian coach is being tipped to leave Stamford Bridge at the end of the season, despite making a huge impact on the club.
Conte led Chelsea to the Premier League title last year after taking over in 2016 but has never had an easy relationship with the Chelsea hierarchy and is now fully expected to move on.
The Daily Mail report that Chelsea have already started work on finding his replacement and have identified managers who could take the helm in West London.
Juventus manager Max Allegri and former Barcelona coach Luis Enrique are the leading contenders, it’s claimed.
Allegri has won three Serie A titles in Turin, however his contract runs until 2020 which could make him difficult to prise away from Juventus.
Enrique quit as Barcelona manager last summer having led them to two La Liga titles and the Champions League during three years at the Nou Camp. He’s thought to be interested in working in the Premier League.
Also under consideration is Maurizio Sarri, the current boss of Serie A leaders Napoli.
The Daily Mail report that the name of Diego Simeone has also come up, but Chelsea believe he will be tough to prise away from Atletico Madrid.
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One manager not under consideration is former boss Carlo Ancelotti. The Italian has been linked with a return to the club, however the Blues do not see him as an option. The man who delivered the double to Chelsea in 2010 has recently been linked with Arsenal.
Conte has been strongly linked with taking over at Paris St Germain, while reports that Zinedine Zidane could be moved on at Real Madrid will lead to talk of him taking over at the Bernabeu.