United said the club received a bid, reported in the British media to be about £25 million (almost Dh141m), but it was "immediately rejected".
"Our position remains that he is not for sale," the club added.
Jose Mourinho, the Chelsea manager, 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.
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