Jose Mourinho has already seen one offer of around £20m for the England striker turned down but an improved sum in the region of £30m has been given equally short shrift.
Mourinho admitted last month that Rooney was 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.
United boss David Moyes has repeatedly insisted that the 27-year-old is not for sale and a club spokesman reiterated that hardline stance on Monday morning.
"A bid was received yesterday (Sunday) and immediately rejected," the spokesman said. "Our position remains that he is not for sale."
Rooney, who has two years left on his current deal, is expected to board a flight to Sweden on Monday afternoon, ahead of United's pre-season friendly against AIK in Stockholm on Tuesday.
Moyes reportedly angered Rooney when he suggested the England star would be needed 'if for any reason we had an injury to Robin van Persie'.
Graeme Souness believes Manchester United have backed themselves into a corner with their handling of the striker, but will not sell him to a Premier League rival.
He said: "Whether it was intentional or unwise words by David Moyes, if I'm Wayne Rooney I'm thinking 'hang on, I'm the star of the show'.
"He sees himself as now second fiddle to van Persie. He will be a very unhappy young man at that - his ego's been dented.
"Manchester United have put themselves in very difficult situation, but I don't think they can sell him to an English team."