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His guilty plea to the lesser charge was accepted by the prosecution at Teesside Crown Court on Monday.
Judge Tony Briggs told the player: "All sentencing options, including custody, remain open."
The court heard Mr McGuinness, 38, was attacked with a beer glass in the Walkabout bar in Bradford in September 2002.
He needed 48 stitches in 10 separate wounds at Bradford Royal Infirmary.
Pryce's plea was accepted on the basis that he felt he was acting in self defence.
Prosecutor Jonathon Devlin said: "Effectively it's the defendant's perception that he was under attack.
"There was evidence from independent witnesses that the complainant, Mr McGuinness, did make a grab at him at one stage."
Pryce was bailed to reappear before the court for sentencing on 10 November.