Conte and Mourinho clashed after Chelsea's 4-0 win over Manchester United at Stamford Bridge last season, with the Portuguese accusing his rival of attempting to "humiliate" the visitors with his exuberant celebrations.
Conte's jab followed Mourinho's assertion that other managers act like "a clown" on the touchline, per Samuel Luckhurst of the Manchester Evening News. "Because I don't like to speak about the other coaches, the other players".
Antonio Conte's Chelsea are now third in the EPL standings as they are one point behind José Mourinho's Manchester United.
"I don't blame him".
"Probably the journalist wanted to say that but didn't have the courage so he said "Mourinho said you behaved like a clown".
The Chelsea manager responded in a due manner by saying, "I think maybe he was talking about himself in the past".
Those words prompted an acerbic response from Mourinho referencing Conte's history of facing accusations relating to match-fixing.
"Maybe sometimes, someone forgets what they said or his behaviour and sometimes I think there is, I don't know the name, "demenza senile", when you are a bit".
"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, hopefully".
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This is a reference to the time when Mourinho ran down the Old Trafford touchline during his visit there as FC Porto manager in 2004.
"Because the question that comes to him is completely wrong, and because of that, he had that out of control reaction".
The most contentious of Conte's comments came when he used an Italian expression, "demenza senile" - senile dementia.
"I was asked about my passion and, you know, I was speaking about myself and then the question to the Chelsea manager was that I said he behaved like a clown", said Mourinho.
But Conte was quick to remind Mourinho that he was once rather similar.
He said: "Look, I don't blame him".
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.
Conte was acquitted in 2016 of charges of not stopping a match-fixing scandal when in charge of Sienna in 2011, per Reuters (h/t Sky Sports).