Chelsea fail in second bid for Rooney
Chelsea made an offer thought to be around £25 million ($38.5 million) but it was immediately rejected.
A United spokesman said: "A bid was received yesterday and immediately rejected. Our position remains that he is not for sale."
The second bid and United's swift response could prompt Rooney to hand in an official transfer request.
New Chelsea boss Jose Mourinho has made the 27-year-old his top transfer target, but United have had trouble signing other players this summer and have been frustrated by their pursuit of Barcelona's Cesc Fabregas.
United's new manager David Moyes has repeatedly stressed that Rooney is not for sale. Rooney himself is believed to have been unhappy at Moyes' remarks that he would effectively have to be understudy to main striker Robin van Persie.
United later announced that Rooney would not travel to Sweden for Tuesday's friendly against AIK Fotboll.
The striker injured his shoulder in Saturday's behind-closed-doors game against Real Betis, the club said.
This is the second injury to have affected Rooney in pre-season after he flew home from Thailand earlier in July with a hamstring problem.
But Moyes insisted Rooney's injury was not serious, and the former Everton player could yet return in Rio Ferdinand's testimonial on Friday or the Community Shield against Wigan at Wembley on Sunday.
"Wayne hurt his shoulder in a fall during a match on Saturday," Moyes told United'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."
Meanwhile, United's pursuit of Spain midfielder Cesc Fabregas appears to have stalled with Barcelona sporting director Andoni Zubizarreta claiming the champions have accepted he is staying at the Nou Camp.
United defender Ferdinand added: "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."
Related Manchester United News