However, Mourinho seemed to suggest otherwise, telling reporters how he has never been suspended for match-fixing, which upset the Italian.
The two men have been embroiled in a public dispute over the last week, as Chelsea manager Conte branded his opposite number "a little man" who has a bad memory. I consider him a little man, a man with a very low profile.
"I swear, as captain of the football club, I was there thinking: 'Why has he not spoken to me?' I said to the physio: 'I'm training tomorrow". The 47-year-old then insisted that his star man is happy at Stamford Bridge.
The Premier League rivals have been involved in a war of words after Mourinho's comments that he preferred to act more mature on the touchline were perceived as a dig at the Chelsea coach. Mourinho famously wore a t-shirt to show his support for the ousted Foxes manager after he had led the club to a heroic Premier League title victory in 2015-16.
Mourinho took their rivalry to the next level on Friday evening when he had a dig at Conte's past.
"You can change the story, but you have to know the story very well before hurting another person".
"Maybe, sometimes, I think that someone forgets what's said in the past, which is his behaviour".
"I have this look of a person that regrets?"
Later speaking to BBC Radio 5Live, Conte added: "When is the game against United?"
"I think it's not important, the association, you understand".
Conte's stance ensures that all eyes will be on the Old Trafford touchline when Chelsea take on United in the Premier League on February 25, but the Italian has a more pressing challenge to navigate first as he prepares for a two-legged Carabao Cup semifinal tie against Arsenal.
Asked if the League Managers' Association (LMA) should now step in to try to fix the damage between Conte and Mourinho, the Chelsea boss said: "I think it's not important, the association, you understand".