The Germany international made his £42.4m switch to the Gunners on transfer deadline day - but the report claims United made a bid to bring him to Old Trafford.
United representatives made a late call to Özil's agent to gauge his interest in moving to the Premier League champions - only to be told that his move to Arsenal was all but done.
The club has publicly denied ever making a move for Özil, but admitted interest in the 24-year-old ex-Real Madrid playmaker earlier in the summer.
Still, a Manchester United Evening News source told the paper: "United made a call. Kenny Moyes, David's brother who is an agent, was trying desperately to get hold of Özil's agent.
"I think that by that time they managed it, it was too late."
Özil has since established himself as a fan favourite at the Emirates Stadium, and has quickly taken to life in the Premier League.
So it won't come as welcome news to United fans to find out that - as well as missing out on the likes of Cesc Fabregas, Thiago Alcantara and Fabio Coentrao - they failed in their Özil pursuit too.
It was a haphazard first transfer window for new boss David Moyes, with the club missing out on several midfield targets, only to secure a deadline day move of their own for Marouane Fellaini.