The 48-year-old unexpectedly quit Serie A giants Juventus to manage his country in the wake of the 2014 World Cup.
And he subsequently guided them to the quarter-finals of Euro 2016, only to be knocked out on penalties by Germany.
Conte had already decided in April 2016 not to continue as Italy coach after last summer's tournament because he fancied a return to club management.
And he made his mark during his first 12 months in English football, leading Chelsea to the Premier League title and FA Cup final last term.
Conte's relationship with top brass at Stamford Bridge has not been the best since the turn of the year though.
And The Sun claim Italian chiefs are hoping to lure him back to his homeland to replace Gian Piero Ventura.
Italy's current gaffer led them to second place in World Cup qualifying Group G behind 2010 champions Spain.
And they now face the lottery of the play-offs to decide whether they'll be competing in Russia next year.
Senior officials in the Italian FA are apparently lobbying for Conte to return to the helm.
And The Sun indicate that could even happen before the 2018 World Cup takes place.
Ventura is under contract with Italy until 2020 - with Conte tied down at Chelsea until 2019.
The fact he declined to extend his stay in west London this summer though, coupled with recent comments, suggests Conte may fancy a comeback with the 2006 world champions.
Last month, Conte said: "I have nostalgia for Italy.
"Once I have had some more nice experiences I will return to Italy, for sure.
"I don’t know when, but the goal is to do that."
Conte was known to have united the Italy dressing room during his time in charge of the national team.
And Ventura may be shown the door fairly promptly amid speculation that there have been a series of rifts in the camp.
Conte's current focus will on Saturday's return to domestic action, though.
Chelsea travel to bottom club Crystal Palace for a 3pm kick-off.
