The experienced England attacker is out of contract in the summer, after a mooted summer transfer to West Ham United did not go through.
According to The Sun, Lingard has turned down the most recent contract offer from United to extend his current deal.
If nothing changes, the 28-year-old will leave United in the summer on a free transfer, and he can speak with other clubs from January.
Lingard did come on for United against Newcastle United in the Premier League on Saturday, scoring the last goal in a 4-1 win.
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