Jose Mourinho has already seen one offer of around £20million for the England striker turned down but an improved sum in the region of £30million has been given equally short shrift.
A United spokesman said: "A bid was received yesterday and immediately rejected. Our position remains that he is not for sale."
Mourinho has admitted that Rooney is his sole summer target, while the player himself is reportedly ready to try and force through a move by handing in a written transfer request.
"A bid in the region of £30m has been made and it is our information that bid has been rejected," Sky Sports' Dharmesh Sheth said.
"The question now is whether Chelsea will go back with a third bid. It looks like Chelsea want Wayne Rooney and it looks like they want him quite badly."
Rooney, who has two years left on his current deal, will not travel to Sweden for the friendly against AIK Fotboll on Tuesday night after injuring his shoulder in Saturday's behind-closed-doors game against Real Betis, the club have confirmed.
A post on the club's official feed read: "@WayneRooney misses out on the final #mutour match due to a shoulder injury sustained at the weekend. David Moyes: "It's not too serious."