The 21-year-old has been suspended by the club since January 2022 after accusations of attempted rape and assault.
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Greenwood was arrested and charged, but charges were dropped by police at the beginning of February 2023.
United have been conducting an internal investigation and he is not expected to return to training until next season at the earliest.
However, as reported by The Sun, Greenwood has told his friends that he will never play for the club again.
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A source told the news outlet: "Mason believes he's finished at United. He's sat at home kicking his heels and very frustrated.
"He wants to get back playing football but realises his situation is very complicated and it's his own doing.
"He is determined to play football again but doesn't think he'll ever pull on a United shirt ever again."
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United have been weighing up whether or not to bring Greenwood back into the first team picture.
It was reported that he could be forced to conduct a TV interview and undergo therapy before making a return.
However, fan groups, sponsors and the women's team would be consulted before a decision was made.
Players from the women's team have said that they would be 'unhappy' to see Greenwood return.