The former Blues player and coach said: “Conte can’t wait to leave Chelsea, he can’t stand that they sell or buy players without consulting him.”
But, ahead of Chelsea’s London derby meeting with West Ham on Sunday, Conte hit back by claiming he has not spoken to Vialli for some time.
“Don’t forget that now Gianluca Vialli for many years has been working for Sky, he is a journalist,” he said.
“He is a friend but he is a journalist and I have great respect for him but I can tell you I have not been talking to him since one year.
“Now I think his role brings him to say something about my situation. This is not the only person that is doing this.”
“With Gianluca, we played together for many years at Juventus, he was my captain, we won the Champions League together and I consider him a friend. I understand because he is now a journalist and he has to give news to Sky and to try to speak about my situation.
“Those who know me very well, they know me, they know that in this moment I am very angry. I am very sad for this situation.
“Those who know me very well know I am trying to put all of myself to change this situation because I have great responsibility.”