And with Guus Hiddink also leaving Chelsea at the end of the season, the Premier League champions are in the process of lining up a long-term replacement for sacked boss Jose Mourinho.
Italian newspaper La Gazzetta dello Sport are claiming that the London club have agreed a deal in principle with Conte.
And the odds have been slashed on Conte moving to Chelsea.
Express Sport understands Diego Simeone, Jorge Sampaoli and Massimiliano Allegri are also under consideration to replace Hiddink.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy