Rooney was hurt in the final minute of Tuesday night's 2-1 Champions League loss at Bayern Munich. The person, who spoke Wednesday on condition of anonymity because the announcement had not been made, said Rooney had not broken any bones and should be fit for the World Cup.
Rooney flew back to Manchester from Munich on Wednesday with his right foot in a protective boot. He scored his 34th goal of the season in the second minute of the game at Allianz Arena.
England coach Fabio Capello says the injury is "terrible" news. England plays its World Cup opener against the United States on June 12.
"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 against Chelsea at Old Trafford. The result is likely to have a major effect on the title race, with United a point ahead of second-place Chelsea.
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, he would 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 veteran forward until Rooney returns.
"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."