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The pair's relationship on the touchlines and away from it has been an intriguing one over the years, with the spotlight returning to the duo ahead of Saturday's Premier League clash between United and Arsenal.
Mourinho, who has lost only one of 15 previous meetings with Wenger, labelled the Frenchman a "specialist in failure" in early 2014, but there were no such inflammatory remarks on Friday.
The Portuguese does clearly feel though that he is afforded less respect than a manager who last won the Premier League in 2004.
"The records against any other manager being good or bad is not important," Mourinho said.
"For me, the only thing that matters is what you get globally as a team. Our team's results, our CV, if you want to go to that direction.superfly v red
"In the Premier League, tomorrow is a match between the two managers with the best record in the Premier League.mercurial vapor v red
"Sir Alex Ferguson isn't here anymore. Tomorrow, I think between the two managers we are speaking about, I think (we have) six or seven Premier League titles (between us). I have three, he has three or four.
"Does that mean we should be respected, even in periods where our results are not the best? I think Mr Wenger has that respect from all of you, I don't think I have, especially because my last Premier League title was 18 months ago, not 18 years ago.
"I don't think I get that respect. But to be honest, I just follow my way because I want to win a ninth championship and I want to win a fourth Premier League."
To do that Mourinho could do with a morale-boosting win on Saturday, with fourth-placed Arsenal already boasting a six-point cushion over United.
The Portuguese has been criticised in some quarters since taking the Old Trafford reins, yet the former Chelsea boss insists there is no club he would rather be with right now.
The future of his players has also been a hot topic over the past fortnight after Mourinho appeared to take aim at Luke Shaw and Chris Smalling following United's 3-1 win at Swansea.mercurial superfly cr7 blue
The players' pain threshold came into question but both missed out on the England squad because of injury problems, with Shaw understood to have been suffering pain in the leg that was so horrifically fractured in two places back in September 2015.
The left-back is fully fit again but could be overlooked against Arsenal, while it was reported that Smalling may not play again before Christmas having broken a toe in two places.
"I don't say a word about Chris Smalling," Mourinho said sternly.
"You have your sources, you trust your sources, you do the big headlines with your sources and now I am not interested in commenting on that.
"Luke Shaw I will comment on, yes. He worked well in this period where we had a very small group, which is not the best but he worked really well.16+ PureChaos white
"He is ready to play. I don't have any problem with him, I am not saying he plays or he doesn't play tomorrow.
"I am saying that he is my player, a young player with potential. A young player like every young player with little problems, with things that needs to learn, with things he needs to improve.
"But he is a player of my confidence and playing now five matches in two weeks like we are going to do, in three different competitions, for sure he is going to play."