In a video clip, Robson can be seen with blood oozing out from her lips.
Mason Greenwood's audio and video of assaulting his girlfriend are going viral.
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A voice note purporting to be of an attack was also posted.
The police did not name Greenwood, but the statement about the investigation was provided after inquiries about the footballer.
They were both axed from the squad and will miss the clash against Denmark tonight after the video revealed they had breached strict quarantine rules set for the squad.