Allegri signed a new contract at Juventus previous year which ties him to the Turin club until 2020. This season Chelsea stand no realistic chance of defending their crown, but could win at least one cup competition.
The Italian won the Premier League title last term, in his first season as head coach with the Blues, who play Leicester on Saturday.
"I have another year of (my) contract with this club", he said.
The Serie A champions are ready to let the 26-year-old leave the Allianz Stadium as they have identified Bayer Leverkusen's Wendell as his potential replacement. "I don't think so", said Conte. As I said before I am always telling the same things.More news: England skipper Root in hospital with severe dehydration
The Chelsea boss has vowed "I won't forget" Mourinho's criticism, after the Manchester United manager hit out at Conte over match-fixing.
The genesis of this set-to harks back to October 2016, when Conte appeared to antagonize Mourinho, the self-styled "Special One", in United's 4-0 defeat at Stamford Bridge. I can give my opinion to my club for every situation, but then they have to make the best decision and that is right. So wrong question and obviously a strong answer and I don't blame. Later, Conte added: "I am starting to be a bit annoyed. I consider him a little man and I consider him a man with a very low profile". Gennaro Gattuso is by no means guaranteed to remain in his post as Milan boss either, meaning there may be an opening at San Siro for the former Juve man.
Chelsea are now undefeated in nine matches but Wednesday night's League Cup semi-final stalemate at home to Arsenal makes it three draws in a row for a side that is sorely lacking the tactical variation required to break down stubborn opponents.
With only 41 Premier League goals this season, Chelsea have scored less than any of their top-four rivals and lag 16 points behind leaders Manchester City.