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.
Without naming names, Mourinho appeared to aim a dig at Conte and Liverpool manager Juergen Klopp - two of the most animated and passionate coaches in the Premier League - by saying on Thursday he did not feel they need to behave like "a clown" on the touchline.
Quizzed on those comments, Conte hit back at Mourinho on Friday afternoon by using the Italian phrase "demenza senile", which translates as senile dementia. "Maybe, sometimes, I think that someone forgets what's said in the past, which is his behavior", Conte said. Conte said. "Maybe sometimes I think that someone forget what they said in the past or which is his behaviours and sometimes I think there is, I don't know the name, demenza senile, when you are a bit [Conte taps his temple] when you forget what you do in the past".
The former Chelsea and Real Madrid manager has been linked with a switch to Paris Saint-Germain recently. The refereeing decisions were a bit odd. I could talk about the refereeing decisions against us for a month but I won't since you have to respect these decisions.
"Wenger must to find this way [accepting decisions]; it's not good, it's not good".
"For the other situation, I am repeating - there is a person who continues to look here".
"I think Wenger has to accept the decisions". You understand? He went away, but he continued to look here.
Conte also took aim at Wenger, who has been particularly vocal about the standard of refereeing in the Premier League in the last week.