United said Monday the club received a bid, reported in the British media to be about 25 million pounds ($38.4 million), but it was "immediately rejected."
"Our position remains that he is not for sale," United said.
Chelsea manager Jose Mourinho confirmed last month that the London club had made an official cash bid for Rooney.
The England international has been pushing for a move since expressing his frustration to United about his lack of playing time toward the end of last season.
But both Alex Ferguson and David Moyes, who succeeded his fellow Scot as manager in May, have insisted Rooney is not for sale since he has two years left on his contract.
United also said that Rooney would not travel to Sweden for a pre-season match against AIK in Stockholm on Tuesday after injuring his right shoulder during another friendly.
"Wayne hurt his shoulder in a fall during a match on Saturday," Moyes said. "It's not too serious and I don't expect it to keep him out for too long. I'm disappointed he's missing the game because we were keen to get him back involved and ready to play."