Red Devils insist though that Englishman is not for sale and will still be at the club next season.
Chelsea are said to be readying a second improved bid of £40 million for unsettled Manchester United front man Wayne Rooney, with the player himself thought to be desperate to make the move to Stamford Bridge next season to work under returning Blues head coach Jose Mourinho, reports the Mail on Sunday.
The west London club have already had one offer of £30m for the England international rejected out of hand by the Red Devils, who remain adamant that the 27-year-old is not for sale this summer at any price and will still be at Old Trafford come the start of the new Premier League season.
However, officials at United are bracing themselves for the imminent arrival of a second improved bid for Rooney, who is understood to want to quit the Premier League champions so as to be able to reignite his career in the capital.
Rooney is still hurt by the actions of previous United manager Sir Alex Ferguson, who claimed at the end of the previous campaign that the striker had handed in a transfer request, a suggestion that the player himself strongly denies.
But it is also believed that it is the chance to be first-choice striker at the Bridge, which Mourinho is offering Rooney, that is the decisive factor in him wanting to quit United after nine years in the north west, during which time the Englishman has netted 197 goals in just 401 appearances for the club.