Recent reports suggested that the Blues had offered the Premier League champions either Juan Mata or David Luiz in a cash-plus-player deal.
However, Chelsea have now revealed that they only made a cash offer in writing.
"Chelsea Football Club can confirm that yesterday it made a written offer to Manchester United for the transfer of Wayne Rooney," read an official statement.
"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."
United managed David Moyes claimed at the start of the month that Rooney was not for sale.