The MLS side are seeking a big-name replacement for Wayne Rooney, who will return to English football with Derby in January.
United officials have held talks with Ozil's representatives in the United States in recent days.
The former Germany international was not always a regular starter under Arsenal boss Unai Emery last season.
And with Nicolas Pepe and Dani Ceballos having joined the Gunners' ranks this summer, there are doubts over how much meaningful action Ozil will get in 2019/20.
The former Real Madrid playmaker missed Saturday's 2-1 defeat of Burnley due to illness.
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