The Sun reports United are keen to bolster their midfield options, with Paul Scholes and Ryan Giggs in the twilight of their careers and Owen Hargreaves still struggling with injury.
The 25-year-old Diarra cost Madrid £20 million when he joined from Portsmouth two years ago.
But the suggestion is United could get the French international for considerably less, perhaps around £12m.
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Caughtoffside is always good for an outrageous rumour and today's no different.
They're linking Juventus with a £27m move for Arsenal's Robin Van Persie. Apparently Juve may also be willing to throw Felipe Melo in as a makeweight.
Arsenal have yet to comment.