The England striker was hurt in the final minute of Tuesday's 2-1 Champions League loss at Bayern Munich. The person, who can't be identified because the news hasn't been officially released, told The Associated Press that Rooney hadn't broken any bones.
Rooney scored his 34th goal of the season in the second minute of the game at Allianz Arena.
Although Rooney is expected to be fit for the June 11-July 11 World Cup, England coach Fabio Capello said the injury was terrible news.
"I think he will have a scan tomorrow," Capello said Wednesday. "I'm not happy when a player from the England team is injured, it's terrible. It's not a good thing for me. I will speak to him this evening or tomorrow morning."
Rooney is set to miss Saturday's Premier League match with Chelsea at Old Trafford. The result is likely to have a major effect on the title race, with United a point ahead of Chelsea at the top of the standings.
An absence of two weeks would rule Rooney out of three games: league matches against Chelsea and Blackburn and the Champions League return leg against Bayern.
Three weeks would mean Rooney also misses the derby at Manchester City. If out for a month, the striker will be sidelined for the league game against Tottenham and possibly a Champions League semifinal against Lyon or Bordeaux - if United qualifies.
With Michael Owen out for the rest of the season, United is left with Dimitar Berbatov as the team's only senior forward until Rooney returns.
Rooney flew back to Manchester on Wednesday with his right foot in a protective boot, returning to some gloomy headlines in the papers.
"England's worst nightmare" said The Times, while the mass circulation Sun had one word: "Pray."
"Get well soon" said the Daily Mail alongside a photo of Rooney grimacing and lying on the turf in pain. "Please don't let this be the moment England's World Cup dream died."
