06 August,2013 01:44 AM IST | | Agencies
Chelsea made an offer thought to be around 25 million pounds (USD 38.5 million) but it was immediately rejected.
Wayne Rooney
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.
