Chelsea put forward an offer for the England international on Sunday, thought to be around £25million, but it was immediately rejected.
A United spokesman said: "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.
Meanwhile, Rooney has pulled out of the pre-season trip to Sweden with an injured shoulder
The club said Rooney had injured a shoulder in the behind-closed-doors game against Real Betis on Saturday but that has caused inevitable speculation that it was a convenient injury while his future remains uncertain – something United strongly deny.
Some reports state Rooney is now considering making an official transfer request though it is unclear if that would help his cause, having already told the club he wants a move – and it would further alienate United fans.
United manager David Moyes insisted Rooney’s injury was not serious, and there are other matches coming up including Rio Ferdinand’s testimonial on Friday and the Community Shield against Wigan at Wembley on Sunday.
"Wayne hurt his shoulder in a fall during a match on Saturday," Moyes told the club’s website. "It’s not too serious and I don’t expect it to keep him out for too long.
"I’m disappointed he’s missing the game because we were keen to get him back involved and ready to play."
Chelsea boss Jose Mourinho has made the England striker his top transfer target and Rooney told former United manager Sir Alex Ferguson last season that he wanted a move.
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.
This is the second injury to have affected Rooney in pre-season. The player flew home from Thailand earlier in July with a hamstring injury.
Meanwhile, United’s pursuit of Cesc Fabregas appears to have stalled with Barcelona sporting director Andoni Zubizarreta claiming the Barclays Premier League champions have accepted that he is staying at the Nou Camp.
Rio Ferdinand also insisted he too was in the dark over Fabregas, saying: "I don’t know what’s happening, we just listen to the news and read everything online and wait and see. Any quality player that comes to Manchester United is welcomed with open arms and he is a quality player."
Ferdinand is not in the squad to go to Stockholm either and Nemanja Vidic will skipper the side in Sweden after missing the first leg of the tour due to a sciatica problem, while Portuguese winger Bebe, signed for £7.4million in 2010 but who has yet to start a game in the Premier League, is also in the squad.
Manchester United squad: Lindegaard, Amos; Rafael, Evans, Evra, Jones, Smalling, Vidic; Anderson, Bebe, Carrick, Giggs, Nani, Zaha; Henriquez, Kagawa, Van Persie, Welbeck.