Rooney suffered a deep gash in his forehead during a collision with team-mate Phil Jones at the club's Carrington base on Saturday and needed stitches, the Sunday People reported.
He was caught in the face by Jones's studs and, after extensive treatment at the medical centre, he joined his team-mates - who had since travelled by coach - at their Liverpool hotel later in the day.
However he was not on the team bus that arrived at Anfield on Sunday lunchtime.
The injury could see the 27-year-old striker miss England's upcoming crucial World Cup qualifiers against Moldova and Ukraine, the paper said. England face Moldova at Wembley on September 6 before travelling to Kiev to play Ukraine on September 10.
Rooney, who was coveted by Chelsea boss Jose Mourinho and expected to leave the club until recently - he was upset that Robin van Persie was publicly backed by United boss David Moyes as the club's first-choice striker, with the Liverpudlian seen as a back-up option - featured for United in the goalless draw against the Blues a week ago.
He was afforded a generous reception by the home fans inside Old Trafford, and Moyes has since said he can still elevate himself to the status of an Old Trafford legend.
"There is a situation with Wayne where he could go on to emulate some of the greats at United with the goals he can score," Moyes said. "The challenge is there. We've said it openly - he's got an opportunity to reach the great heights here.
"I wouldn't say the heights of immortal people, but those like Sir Bobby Charlton are on as high a pedestal as anybody can get.
"We've set it down for him - can you put yourself in this position? Judging the crowd reaction last week, they would all be happy as well."
Rooney only requires three more goals to become the fourth player to score 200 for United. Charlton is the club's all-time leading scorer, with 249.
Reports have indicated that Rooney has no problem with Moyes, despite the pair's relationship also having broken down when the striker moved from their former club Everton to United in 2004.
And the Scot said that he did not have an issue with the player.
"I've read all this stuff about what was supposed to have happened, but I've never had a minute's problem with him," said Moyes.