Mourinho is under pressure heading into this weekend's clash with his team already eight points off the pace in the Premier League.
Much of the build-up to the game has centred on Mourinho's personal rivalry with Wenger and the United boss insists the Frenchman receives more respect from the British press, despite the fact the two managers have won the same number of Premier League titles.
"Sir Alex Ferguson is not here anymore and tomorrow we are speaking about six or seven Premier League titles," Mourinho said at his pre-match press conference.
"I have three and Mr Wenger has three or four, I don't know. We are speaking about the two managers with the best record in the Premier League.
"Does that mean we should be respected, even in periods when 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 and not 18 years ago. So I don't think I get that respect."
Wenger is yet to beat Mourinho in the Premier League but the United manager insists that statistic will have no bearing on this weekend's game.
"The record against any other manager being good or bad is not important," he said. "The only thing that matters is what you get globally as a team."
Mourinho guided his former club Chelsea to the Premier League crown just two seasons ago and is determined to recreate that success at United, despite the club's slow start to the campaign.
The Portuguese insists he is happy at Old Trafford and says he turned down a number of offers from across Europe in order to take charge of the Red Devils earlier this year.
"I am in the club where I want to be. That's as simple as that. When I was sacked at Chelsea I was not in trouble. I had lots of offers," he said.
"I don't speak about them because it's a matter of principle but I could have been working one week after. I could have been working immediately.
"I could be working in some of the biggest clubs in Europe and I waited for the chance to work at a club I wanted to be.
"I was champion at four different clubs and I want to be champion in every club I work, which is quite a nice record if I can do that. So I want to do that at Manchester United."