Wenger, who has had a tempestuous relationship with Mourinho, announced on Friday that he will call time on his 22-year association with Arsenal at the end of the season.
However, with Wenger set to take Arsenal to Old Trafford for the last time on Sunday, the Manchester United manager is keen to draw a line under their chequered past.
"If he respects me even 50% of what I respect him we can even be friends in the future," Mourinho told Sky Sports News. "I have lots of respect for him.
"But the reality is that he was at Arsenal, he was the champion and I came to the country in 2004 and wanted to steal his title. That's football.
"But in the end I respect him a lot, I tried to show that in the past couple of years there were no more problems at a different stage of my career with a different profile.
"I feel sorry that after Sir Alex Ferguson - but it was obviously Sir Alex's decision [to leave] - the next big one, the next iconic one is leaving the Premier League."
Man United are second in the Premier League table with four games to play, 16 points behind champions Manchester City, while Arsenal are sixth.