However, the ex-England international will have to take a pay cut as his wage demands are too high for the MLS side.
DC United have been linked with Arsenal playmaker Mesut Ozil as they seek a big-name replacement for Wayne Rooney.
The former Manchester United man will leave MLS to take up a player-coach role at Derby in January.
Sturridge was earmarked as another potential successor, but United are unable to pay him his desired salary.
The 29-year-old is still without a club after being released by Liverpool at the end of last season.
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