"What has never happened to me and will never happen is to be suspended for match fixing".
Asked if other managers' comments annoy him, Conte replied: "I must be honest - I don't read [any of it]".
Mourinho claimed he did not need to act like a "clown" to prove his desire to stay at Manchester United, saying his commitment to the club is "total".
"Probably the journalist wanted to say that but didn't have the courage to say that, so he said that Mourinho said that you behave as a clown".
After Chelsea's draw at Norwich the Italian labelled him a'little man after his recent jibes
It's prompted Conte to call on Mourinho to remember his own history: "I think that he has to see himself in the past, maybe he was speaking about himself in the past, yeah?"
Initially, Mourinho appeared to be backing Conte following the furore caused by his words on Thursday - only then to make the reference to match-fixing. Maybe sometimes, someone forgets what they said in the past, or [forgets] his behaviours. Conte, clearly feeling that Mourinho was referring to him, suggested that the former Blues boss was suffering from a form of dementia.
Or a similar incident while Mourinho was in charge of Chelsea, when the London club scored late to eliminate Paris Saint-Germain from the Champions League in 2014. I'm not free of that, especially if we score a winning goal in a specific moment I am not free to have an out-of-control reaction. I was speaking about myself, saying I don't need to behave as a clown to show passion, that I control my emotions in a better way, everybody knows I don't need the Chelsea manager to say that I made mistakes in the past, and I will make in the future.
Conte has been vocal in recent weeks about improving the depth of his squad in January, and Chelsea made their first signing on Friday, moving swiftly to acquire Ross Barkley for £15 million from Everton.
Following last night's 2-0 triumph over Derby County, the Portuguese tactician conceded he wishes to end the minor squabble he commenced by adding managers shouldn't behave like clowns on the touchline. Conte, who is an animated figure on the touchline, was asked about the quote at his pre-match press conference and suggested Mourinho - who has wildly celebrated goals in the past - has "demenza senile".