Conte left the Azzurri role after Euro 2016 to join the west London club but a recent radio interview in Italy, in which he admitted he missed his native country, has prompted suggestions he will return to take charge of the national team at the end of the season.
Neither himself, nor the Chelsea hierarchy, appeared willing to fully commit to each other.
Last month the Italian was reported to have told a radio station that he has "a longing" to return to his homeland and is not keen to "stay overseas for too long".
Conte insists his comments were interpreted.
It was claimed that Conte was being considered as a potential replacement for Milan boss Vincenzo Montella, who is reportedly under pressure.
"I did an interview two weeks ago and the translation was wrong", he said.
And while the player has a €100 million release clause in his contract, only foreign clubs are able to trigger it, meaning AC Milan will have their work cut out for them.
'I like to have this great feeling with our fans, our supporters and I don't see problems. My daughter goes to school here.
He said: "Another situation I want to clarify is that my family stay here with me, not in Italy".
"It is important to say the truth, my family stays here, not Italy".
"Every coach, when they start, they work with the club and hope they will stay for a long time and build something important".