Conte let loose following Chelsea's FA Cup third-round draw against Norwich City on Saturday as the Italian said Mourinho was a "little man" for referencing the match-fixing scandal that he was caught up in during his time in Italy but later fully acquitted by a court from.
And, when asked in his post-match press conference for more reaction to Mourinho's latest jibes towards him, Conte insisted he is ready to talk to the Portuguese when Chelsea take on United next in the league on 25 February.
"The situation is very clear. I don't have anything to clarify," Conte told reporters.
"It will be the opportunity in the game against United when we go to Old Trafford.
"Me and him face to face. I'm ready. I don't know if he's ready.
"I consider him a little man, I consider him a man with a very low profile.
"When there are these types of comments, before (making them) you have to know very well the truth.
"Before you make this type of comment, before to hurt another person, you must pay great attention. You show you are a little man.
"I know him very well in the past. In the past he was a little man in many circumstances, is a little man in the present and for sure he will be a little man in the future."
Conte then added: "He offended [Claudio] Ranieri for his English. Then when Ranieri was sacked [by Chelsea] he put on a shirt (with initials on) for Ranieri. You are a fake.
"If you want to fight a person, you try to kill this person. And then after two years you try to help this person, because maybe it's good for you, for your profile."