The Bianconeri have become alarmed after their head coach hinted that he is disillusioned with the Italian game amid reports the Blues could swoop for the 43-year-old
Conte's display of anger at his press conference after the 2-0 victory at Bologna on Saturday has put the club's board on high alert, with Chelsea and Real Madrid thought to be considering the former Juve midfielder as a possible answer to their coaching quandries this summer.
The 43-year-old, who had earlier been chastised by opposition coach Stefano Pioli for over-exuberant celebrations at the full-time whistle, used his media commitments as a platform to air his grievances with some of the ills in the Italian game at present.
"It would be easier to pack up and leave [to another country]," said Conte. "As our bus pulled into the stadium, there were people holding children in their hands, and at the same time cursing against us. Similar things happened in Florence and Naples: spitting, throwing sticks and rocks. What's going on here?"
And the coach's latest blast has been met with concern in the boardroom at Corso Gallileo Ferraris. Club chiefs are worried that Conte could be set to decide enough is enough, after expressing previous problems in relation to his four-month touchline ban for failing to report match-fixing and the victimisation of the Old Lady by referees.
The former Arezzo, Bari and Atalanta coach has been with the Turin outfit since leaving Siena in the summer of 2011, winning the Scudetto last term, while leading his side to the Champions League quarter-finals and to the brink of a second successive league title this season.
Conte's record has made him one of the most sought-after young coaches in the game, and his latest comments have had tongues wagging over interest from Chelsea, who will release interim boss Rafa Benitez at the season's end, and Madrid, whose three-year relationship with Jose Mourinho looks set to terminate in the summer.
As a result, president Andrea Agnelli could now launch a pro-active move against possible interest from big-money foreign clubs by inserting a multi-million euro buyout in Conte's current deal, which is set to run until 2015.