The two managers have enjoyed a spiky relationship since the Portuguese arrived as manager of Chelsea in 2004 and deposed Arsenal's "Invincibles" as champions.
Famously, Mourinho called Wenger a "voyeur" and a "specialist in failure" while, in the early days of their feud, in 2005, Wenger responded by calling Mourinho "stupid" and "disconnected with reality".
As recently as October 2014, the two managers were involved in an ugly touchline row that saw them almost come to physical blows in a game between Arsenal and Chelsea -- an example of the sort of behaviour Mourinho now says he regrets.
"Regrets? Little negative episodes, yes I do and probably he also does," Mourinho told the press at United's training base.
"There are little things where it would obviously have been better without them, some gestures, some words would be better without it. I feel better now without it, no doubt about it.
"But again when I arrived in England 2004, Arsenal was the champion and it was the famous champions of the Invincibles. And I arrived and for the next couple of years was with them -- Bergkamp, Thierry, Campbell, amazing teams. So again thank you very much for that, they pushed us to the limits."
Mourinho said he hoped United fans, who have not always treated Wenger with respect, would give him a good send-off on Sunday.
"I always feel the biggest rivals are our biggest friends because they're the ones that pushed us to the limit," said the United manager.
- Arsenal v Man Utd rivalry -
"And I think Manchester United fans know that until 2004, for about a decade, it was between Manchester United and Arsenal. It was between Sir Alex (Ferguson) and Mr Wenger.
"And I think that these great teams Arsenal had and the fight shoulder to shoulder with Manchester United made Manchester United better and better. I hope he has a good reaction -- if not good, not bad at all, and from us, as a club, he is going to feel the respect we have."
Mourinho could not let the occasion pass without a small dig at his old rival, when he claimed that if United were in the Europa League this season, they would have won the competition.
After Arsenal threw away a lead to draw 1-1 with Atletico Madrid in the semi-final first leg at the Emirates, Mourinho's point was clear.
"Last season we won the Europa League and if we played Europa League this year we'd win it too," he said.
Mourinho, looking to consolidate second place in the Premier League, also stressed that goalkeeper David de Gea is not leaving United.
The 27-year-old Spain international, who is approaching the last year of his contract, has regularly been linked with Real Madrid.
When asked about a potential summer departure for De Gea, Mourinho responded: "No chance."