Battling for second spot behind runaway league leaders Manchester City, Manchester United and Chelsea are separated by just one point in the Premier League table.
The row started when Mourinho was asked whether he was happy at United and responded by saying that he didn't need to act like "a clown" on the touchline to prove his joy.
Those words prompted an acerbic response from Mourinho referencing Conte's history of facing accusations relating to match-fixing. Otherwise I stay silent but I repeat: In this situation, you must have respect and I think that I do this, but at the same time I am starting to be a bit annoyed because once, twice [it has happened]. You said Mourinho said you behaved as a clown.
I think if Arsene watches the game again, he'll understand that he was very lucky in the game with the refereeing decisions, It's odd because I don't like to speak about other coaches or players.
"I don't need Chelsea manager to say I made mistakes in past and will in future".
Mourinho referred to his managerial antics earlier in his career and said he had not lost his passion.
"I know that I celebrate goals running 50 metres, I celebrate goals sliding on my knees, I got celebrations jumping into the crowd". The question iscompletely wrong and because of that it is an out of control reaction. But what I was trying to say is that I behaved badly in the past a few times and in this moment I control myself much better.
"Did he? Not me", the United boss replied. "That never happened to me and will never happen".
The surprising reference to "match-fixing" drew a follow-up question as to whether it was directly aimed at Conte.
Simeone was chased by Chelsea before Conte's appointment in June 2016 but he chose to extend his stay in La Liga.
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).
The former Italy manager - who has always denied any wrongdoing - served a four-month ban in relation to the affair in 2012.
Conte lapsed into his native Italian to explain himself - the phrase he used translates into English as senile dementia, although Chelsea insisted he meant to say amnesia.
In an astonishing scattergun attack, Conte implied that José Mourinho was going senile; called Arsène Wenger an "old coach" who needs to accept refereeing decisions with more grace; distanced himself emphatically from the signing of Ross Barkley and the pursuit of Andy Carroll; and declared himself "ready to fight" anyone who criticises him or his squad.
The Blues' boss further added: "When you forgot what you say in the past, your behaviours, and when you totally forgot, you must be anxious as it means you are becoming old and you need a check".
Conte tapped his temple as he spoke, and was asked to clarify his comment.
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