The first two offers Lyon made for the 22-year-old were promptly rejected by United.
Red Devils boss Jose Mourinho has told Depay that he does not count on him and that he can leave the club, but only if the right offer is received – United were believed to be holding out for a fee of around £16m.
Depay had costed United far more than this, as he arrived at the Old Trafford from PSV Eindhoven in 2015 for a reported £31m.