Officials from the MLS side were in London on Tuesday to meet with representatives of the player, according to the Washington Post.
Ozil was substituted after just 55 minutes of Tuesday's 2-2 draw against Chelsea at Stamford Bridge.
They held more talks with his representatives during a visit to London this week to meet players and agents.
The 31-year-old still has 18 months left on his £350,000-a-week and DC United feel they have a better chance of signing him in the winter of 2021.
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