The bid was rejected and the London club have categorically denied the rumour that Juan Mata or David Luiz were offered to United in part-exchange for Rooney.
Their statement read: "Chelsea Football Club can confirm that yesterday it made a written offer to Manchester United for the transfer of Wayne Rooney.
"Although the terms of the offer are confidential, for avoidance of doubt and contrary to what is currently being briefed to the press in Sydney, the proposed purchase price does not include the transfer or loan of any players from Chelsea to Manchester United."
The England forward is apparently "angry and confused" about his status at United after recent comments made by new manager David Moyes and chief executive Ed Woodward.
And, after Chelsea boss Jose Mourinho spoke last week about how much he admired Rooney as a player, the London club have now placed a firm bid for the 27-year-old.
However, since taking over at Old Trafford, Moyes has stressed that Rooney is not for sale, and the bid has been swiftly declined.
Rooney is currently being treated for a hamstring injury at United's training ground, having had to fly home from the club's pre-season tour.
The stunning development comes less than 24 hours after the depth of Rooney's anger at comments made by United manager David Moyes became known.
With it looking increasingly like Rooney's nine-year stay at Old Trafford is coming to an end, Chelsea have made their move.
That United should dismiss the offer so quickly is no surprise. In recent weeks they have repeatedly insisted Rooney is not for sale, and the idea of selling to a domestic rival is particularly unpalatable.
Yet it is difficult to envisage how United can possibly hold that line right until the transfer window closes.
It increasingly appears Rooney's position is impossible, with United fans likely to turn against their one-time hero.
And for Moyes, it represents a tricky situation given he is attempting to bolster his squad rather than weaken it.
Yet Rooney's reaction to those comments given in a briefing during United's stay in Bangkok last week has been the trigger for a further deterioration in the relationship between club and player.
Though it is thought Moyes did not wish the comments to come across as disparaging towards Rooney, that is exactly how they have been received with the player, now back in Manchester for treatment on a hamstring injury, said to be 'confused and angry' over their content.
The offending words were delivered to Sunday newspaper journalists during a briefing with Moyes in Bangkok last week.
Moyes said: "Overall, my thought on Wayne is that if for any reason we had an injury to Robin van Persie we are going to need him and I want as many options as possible."
As far as Rooney is concerned, he is at the peak of his career and has no intention of playing second fiddle to anyone, or being reduced to the rank of a squad player.
With four Premier League titles and a Champions League winner's medal to his name, the 27-year-old does not believe he has anything to prove at United.
Yet he feels as though he has been put on trial by Moyes at a time when he should be concentrating his efforts on recovering from the hamstring injury that saw him sent home from United's pre-season tour within hours of landing in Thailand on Thursday.
After months of speculation about his future, and no statement of intent to stay from the player, it is now clear that unless there is some major repair work undertaken, Rooney will be leaving.
The manner of United's response is the first major test for Moyes and chief executive Woodward since they replaced Sir Alex Ferguson and David Gill respectively at the beginning of the month.
Former United centre-half Gordon McQueen believes Rooney will now leave Old Trafford, but thinks it would be a big mistake to allow him to join a Premier League rival like Chelsea or Manchester City.
"It would be a big move for Wayne Rooney and one that I hope doesn't happen," McQueen told Sky Sports News. "I hope he stays with Manchester United. Unfortunately it seems to me that the player has got his mind made up that he wants to leave Old Trafford and it looks like to me now that they will probably let him go.
"I think they would prefer him to go to one of the teams in Europe that can afford him - Paris St Germain or Monaco - you certainly wouldn't want him to go to Chelsea or Man City!
"Man Utd did something similar last season and, in my opinion, it won them the league. That was getting a terrific goalscorer from one of their main rivals, Robin van Persie from Arsenal.
"I think it would enhance Chelsea's chances of winning the Premier League if they took Wayne Rooney from Manchester United - just look at the goals he has scored for Man United over the last nine years. They (United) would find that difficult to replace."