The Europa League winners tabled an improved bid for Rooney, having had an initial cash offer rebuffed last month. (Agencies)
"A bid was received and was immediately rejected. Our position remains that he is not for sale," a United spokesperson said.
Rooney left United's recent pre-season tour of the Far East due to a hamstring injury, hours after arriving in Bangkok.
The England striker has also now been ruled of Tuesday's pre-season friendly at AIK Stockholm because of a shoulder problem he picked up in a behind-closed-doors match at the weekend.
According to recent media reports, Rooney has been 'angry and confused' with his situation at United after comments from new manager David Moyes that suggested he was a backup in attack to Robin van Persie.
The former Everton player 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 (USD 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, according to media reports, earns him a basic salary of 250,000 pounds (USD 381,800) a week.
The Europa League winners tabled an improved bid for Rooney, having had an initial cash offer rebuffed last month.