The 27-year-old Rooney has been pushing for a move since expressing his frustration to the club about his lack of playing time towards 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.
Despite those public statements, Chelsea has maintained its pursuit of the England striker, culminating in a formal bid submitted to its Premier League rival.
"The official bid was just about a certain about of money ... Not one single player was involved in our bid," Chelsea manager Jose Mourinho said today after a 1-0 victory over Thailand's all-star team during a pre-season tour of Asia.
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And now Mourinho said United "knows we want the player." "We did what we have to do in a proper way, in an ethical way," said Mourinho, who is back in charge at Chelsea after six years.
Asked whether Chelsea's transfer plans amounted to "Rooney or bust, Mourinho replied: "Yes."
Moyes has made it clear he wants Rooney to remain among the striking options for his first season in charge of the 20-time English champions.
"If for any reason we had an injury to Robin van Persie we are going to need him, and I want as many options as possible," Moyes said at the weekend.