Lingard was expected to leave United at the end of the transfer window having grown frustrated at a lack of minutes under Rangnick.
Newcastle, Tottenham and West Ham were all pushing to sign the 29-year-old in the final hours of the transfer market.
But Lingard was left frustrated as no deal could be agreed before United pulled the plug on his possible exit.
Rangnick has now confirmed that Greenwood's arrest played a part in United's decision to keep Lingard at the club.
Lingard faced some criticism for his decision not to push for a transfer away from United last summer following his successful loan spell at West Ham.
But reports indicated that he wanted to stay and fight for his place, and Rangnick insists that attitude hadn't changed into the New Year.
Lingard only informed Rangnick of his desire to leave United in the final few days of the transfer window.
Anthony Martial, Donny van de Beek and Amad all secured loan moves away from Old Trafford and Rangnick hopes they will be given ample minutes at their new clubs.


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