Chelsea tabled an improved bid for Rooney, having had an initial cash offer rebuffed last month.
"A bid was received yesterday and immediately rejected," a United spokesperson told the BBC. "Our position remains that he is not for sale."
England striker Rooney has been reported to be 'angry and confused' with his situation at United.
He was upset at comments by new manager David Moyes that suggested he was a backup to Premier League top scorer Robin van Persie, and has been the subject of transfer speculation since retired manager Alex Ferguson said at the end of last season that the 27-year-old had asked to leave the club.
Rooney joined United for 27 million pounds ($41.24 million)in August 2004 and has made 402 appearances for the club, scoring 197 goals and winning five league titles and the Champions League.
He has two years left of a contract that earns him a basic salary of some 250,000 pounds ($381,800) a week.
Rooney left the club's recent pre-season tour of the Far East with a hamstring injury, hours after arriving in Bangkok. ($1 = 0.6548 British pounds)
- Sports & Recreation