Police in Manchester, northwest England, said a member of the public had made a formal complaint of assault against the 19-year-old England player.
A spokesman for Rooney denied the allegations.
"Wayne was approached by a man he had never met in an abusive and threatening manner," the spokesman told the Sun newspaper. "Despite extreme provocation, Wayne did not respond."
Local media alleged Rooney, 19, hit a 22-year-old student who taunted him early on Tuesday over his controversial transfer from Everton last year.
The student was reported in the Sun as having said to Rooney: "Once a Blue always a Blue, eh Wayne?".
The reported comment was a reference to a slogan printed on a T-shirt worn by lifelong Everton supporter Rooney before his 27 million pounds ($51.26 million) transfer.
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More than 30 supporters were arrested in clashes after Rooney's return to Everton's Goodison Park at a tense cup match against their English Premier League rivals Manchester United in February.
Rooney, feted in England for scoring four goals to help his country reach the quarter-finals of the Euro 2004 soccer tournament, is expected to play in Saturday's World Cup qualifier against Northern Ireland.