Chelsea put forward an offer for the England international yesterday, thought to be around £25million, but it was immediately rejected.
A United spokesman told the media: "A bid was received yesterday [Sunday] and immediately rejected. Our position remains that he is not for sale."
The second bid and United's swift response will now focus Rooney's mind on his future at Old Trafford - there have been reports that he will consider handing in an official transfer request.
Chelsea boss Jose Mourinho has made the 27-year-old his top transfer target and Rooney told former United manager Sir Alex Ferguson last season that he wanted a move.
New United boss David Moyes has repeatedly stressed that Rooney is not for sale. Rooney himself however was unimpressed by the manager's remarks that he would effectively have to be an understudy to main striker Robin van Persie.