At the time, the Gunners were the defending champions and Mourinho said his aim was to “steal” their title.
With Wenger set to quit at the end of this season, Mourinho insists they can now be friends.
“If he respects me even 50 per cent 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.”