The 2014 World Cup winner is said to be confident he can secure a move to Old Trafford, but it is unclear if United are "willing to push through on a deal for Ozil," per John Cross at the Mirror.
The Germany international is out of contract next summer and therefore able to leave for free.
A switch to Old Trafford would see Ozil reunited with Jose Mourinho, who he knows well from their time together at Real Madrid.
Arsenal manager Arsene Wenger said recently the club could sell Ozil in January if the player fails to extend his current deal, per Jeremy Wilson at the Telegraph.
Former Arsenal defender Martin Keown believes Ozil has already "psychologically" left and should be sold, per BBC 5 live Sport:
BBC 5 live Sport @5liveSport
'Ozil has psychologically left Arsenal' @MartinKeown5 says Wenger should sell the German in January. What do you think? https://t.co/QyjnvC5usB2017-10-4 20:02:52
According to WhoScored.com, Ozil has started just four Premier League games for Arsenal this season and was only a substitute for Saturday's 2-1 defeat at Watford.
Despite a reduced role, the 29-year-old still came in for criticism after missing a good chance to put the Gunners 2-0 up.
ESPN FC's Mattias Karen said Ozil could have handed Arsenal the win in a game they subsequently went on to lose:
Mattias Karén @MattiasKaren
Arsenal may rue that missed chance by Ozil.... Would have killed the game off. Now they must respond. #WFCvAFC2017-10-14 18:01:04
Keown also continued his criticism of Ozil and said the player was also at fault for Watford's late goal, per BT Sport (h/t Dan Ripley at MailOnline).
Ozil's place in the Arsenal team also appears to be under threat and, coupled with his refusal to extend his contract, there is a sense his time at the club may be coming to an end if a buyer can be found.
Per Bild (h/t Sky Sports), the German wrote in his autobiography that he clashed with Mourinho when the two worked together at Madrid.
The Red Devils are also not short of attacking options with Juan Mata, Jesse Lingard, Henrikh Mkhitaryan and Paul Pogba part of a star-studded squad at Old Trafford.
Ozil has done little to impress this season, although Opta highlighted what he is able to offer:
42 - Since his @premierleague debut, Mesut Ozil has provided more assists (42) and created more chances (407) than any other player. Ya. https://t.co/SBeOwr0V3F2017-10-12 09:34:29
Arsenal may be willing to sell Ozil in January, but unless they are willing to sanction a cut-price deal, they may find buyers reluctant—particularly as he will be a free agent come the summer.