The Stamford Bridge club will have to up its initial offer to land the disgruntled England striker and has denied Juan Mata or David Luiz formed part of the initial offer.
United immediately rejected the bid on Tuesday night and insisted Rooney is not for sale, despite the player's desire to quit Old Trafford following the total breakdown of his relationship with the club.
Rooney is understood to have expressed a desire to join Chelsea and the Londoners are expected to return with an improved offer.
Initial reports suggested the west London club was willing to offer David Luiz and Juan Mata in part exchange, but the Europa League holder has strenuously denied either player formed part of the bid.
"Chelsea Football Club can confirm that yesterday it made a written offer to Manchester United for the transfer of Wayne Rooney," a club statement read.
"Terms of the offer are confidential, for avoidance of doubt and contrary to what is apparently 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."
Mata was voted as the Blues' player of the season last term but the Spaniard has been concerned by suggestions new manager Jose Mourinho is willing to sell him, while Luiz starred for Brazil at the Confederations Cup last month.
Rooney is understood to be "angry and confused" following comments by United boss David Moyes suggesting the 27-year-old will be an understudy to Robin van Persie this season.
The England striker's future has been the subject of intense speculation ever since he was left out of United's Champions League last-16 tie against Real Madrid in March, with Goal revealing in May that Rooney was 'hell bent' on forcing a summer move away from the club.
Rooney has two years left on his deal at United but Ed Woodward, the vice-president of the Premier League champion, has claimed the club will not offer him a new contract, while it is prepared to let him run down his current deal.