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The 21 year-old was arrested in January 2022 and was due to stand trial in November on accusations of attempted rape, assault and coercive control.
However, the CPS confirmed on Thursday that all charges have been dropped.
A statement read: "Mason Greenwood was charged in October 2022 with one count of attempted rape, one count of controlling and coercive behaviour and one count of assault occasioning actual bodily harm.
"A decision has been made to discontinue prosecution in accordance with the Code of Crown Prosecutors."
A CPS spokesperson said: "We have a duty to keep cases under continuous review.
"In this case a combination of the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction. In these circumstances, we are under a duty to stop the case.
"We have explained our decision to all parties. We would always encourage any potential victims to come forward and report to police and we will prosecute wherever our legal test is met."
Chief Superintendent Michaela Kerr, Greater Manchester Police's Head of Public Protection, said: "Given the significant media coverage of this case, it is only fair that we share the news that the 21-year-old man, who had been arrested and charged in connection with an investigation opened in January 2022, no longer faces criminal proceedings in relation to this.
"The investigation team has remained in regular contact with the legal team, providing any updates of note, and so understand the rationale for the discontinuation of proceedings at this stage, and that this decision has not been taken lightly.
"Despite the media and public’s interest in this case, we have decided not to comment on it in any further detail."
Greenwood last played for United on January 22 last year in a 1-0 victory against West Ham before being suspended by the club.