The German's contract expires at the end of the season and he will be free to speak to other clubs in winter, unless Arsenal manage to tie him down to a long-term deal.
The Gunners were understood to have offered the 28-year-old a new deal back in February, only for negotiations to be quickly put on hold amid the uncertainty surrounding Arsene Wenger's future.
The Frenchman eventually penned a two-year extension to remain in north London but negotiations over Ozil's contract have not yet resumed and the 2014 World Cup winner could swap the Emirates for Old Trafford.
According to the Independent, Jose Mourinho is "highly confident" of convincing the German to join the 20-time champions of England. The former Chelsea manager and Ozil worked together at Real Madrid, as both arrived at the Santiago Bernabeu in the summer of 2010 and went on to win the Spanish Cup and La Liga in their first two seasons at the club.
The pair left the Spanish capital within three months of each other, with Mourinho returning to Chelsea in June 2013, before Ozil moved to Arsenal for a then club record fee in September of the same year.
However, the pair have remained on good terms since and Mourinho has previously waxed lyrical about the German's ability to understand and implement rigorous tactical instructions. With Juan Mata and Henrikh Mkhitaryan already in the team, United are well stocked in the number 10 role but with the opportunity of signing Ozil on a free transfer might prove too tempting for them.
Meanwhile, former Arsenal midfielder Paul Merson has slammed the German for not working hard enough and has urged Wenger to drop him from the Gunners' starting lineup.
Arsenal are unbeaten on the domestic and European front since their 4-0 defeat to Liverpool in October, since which Ozil has started just one match across all competitions for the Gunners and Merson claims Arsenal are reaping the rewards of dropping him on the bench.
"You look at any world class player in the world we've seen over the last 15 or 20 years – you know one thing they do? They work hard," Merson told talkSPORT.
"They've got the class, they've got the skill, they've got everything, but they work hard at the same time – that's what makes them world class.
"Ozil doesn't do that part of the game, and if you don't do that you can't play in this day and age. The penny has got to drop with Ozil, you can't just play when you're on the ball. And to be fair to Arsene, he's taken him out of the team and they've reaped the rewards in the end."