Conte and Mourinho exchanged angry words on the touchline during meetings between the Blues and United at Stamford Bridge this season.
Mourinho took exception to Conte's antics in the closing stages of Chelsea's 4-0 win in October, while Conte was not impressed with what he felt was deliberate targeting of Eden Hazard during their acrimonious FA Cup meeting last month.
But ahead of Chelsea's trip to Old Trafford on Sunday, Conte says he has no issues with his United counterpart personally and claims he does not enjoy touchline confrontations.
"I have zero problem," he said. "It's a sporting competition between me and him.
"There is a game of football and I want to win with my team, he wants to win with his team. It's normal to be in conflict during the game but only a sporting conflict.
"It's very simple, the conflict is the game. It's not a friendly game, both teams want the three points and for this reason you fight to win.
"Do I like the conflict? No, I don't like it. I prefer to concentrate on my team. But sometimes it's normal for me and the other coach to have this situation. But do I like it? No."
Mourinho was labelled "Judas" by a section of Blues supporters during United's FA Cup defeat, but the man who led them to three titles said afterwards that "Judas is still number one" until someone beats that record.
When asked for his reaction to those comments, Conte said: "Nothing. Nothing.
"He won a lot with this team and this club has always showed him great respect for his past.
"Nothing has changed. We have great respect for his history at this club."
Blues duo Eden Hazard and N'Golo Kante are on the six-man shortlist to be named PFA Player of the Year, but Conte refuses to pick a winner between the two.
Hazard and Kante are up against Harry Kane, Zlatan Ibrahimovic, Alexis Sanchez and Romelu Lukaku for the top award.
"I think it's great for them, it's a great achievement to receive this nomination," said Conte.
"I hope for them to be the best player of the year and also I want them to win the league. Awards are important but the most important thing is if you match the two.
"But I don't like to make a choice between two of my players. It's not right. They deserve the best because they are having a good season, but I think all my players are having a great season."