The Blues' boss thinks the Portuguese coach who's had two stints at the London club merits his place in the club's folklore
Conte, who took over in July after Guus Hiddink had stepped in when Mourinho was fired last term, added that the Portuguese coach who guided Chelsea to three league titles merited his place in the club's folklore.
"I have great respect for him," said Conte.
"He won three championships and I think he was an important man for the club.
"I think he deserves a good reception, because he wrote with the club, with his players, with the staff part of the story of this club.
"When you win three championships, you remain in the heart of the fans. It's normal.
"After the whistle, he becomes like the other players of Manchester United an enemy, in the sporting aspect."
Conte, who guided Italy to the last eight of Euro 2016 losing to Germany in a penalty shootout, will face Mourinho with Chelsea two points better off than United in fifth spot.
Table-topping Manchester City only have a three point advantage over Chelsea whilst United -- who were soundly whipped by their city rivals in the derby earlier this season -- trail by five.
Conte, who established himself among the top tier of club coaches at Juventus a side he also played with distinction for, rubbished claims United would be at a disadvantage because they have played twice this week -- a 0-0 draw with Liverpool and then an easy 4-1 victory over Fenerbahce in the Europa League.
"I don't want this type of advantage," said the 47-year-old Italian.
"This means you don't play in Champions League or Europa League. I think Chelsea must play during the week, this type of tournament."
Conte -- who last week laughed off rumours about him being on the verge of the sack after his odds tumbled at the bookmakers -- will continue to deploy three central defenders which he installed two matches ago after some weak defensive displays saw them leak goals.
Those two games have seen Chelsea not concede a goal.
"I'm pleased, because after many games that we conceded two and sometimes three goals -- and I repeat this is not right, this is not a good way for Chelsea to concede so many goals -- we change it, we change the system of play," said Conte.
"We know we must continue to work and progress in this way.
"I'm pleased because in this week I'm seeing the right commitment, the right work rate for the players. I see players that trust in this system, in this type of work."