The Blues made several offers for the England international over the summer, but were unable to convince the Red Devils to sell, despite the player himself being keen to leave Old Trafford.
Rooney has since settled his differences with the club and has been welcomed back into the starting XI by new boss David Moyes.
But a new contract offer has not been forthcoming, leading to speculation that he may be allowed to move on in the New Year.
This has alerted Chelsea boss Jose Mourinho, who is desperate to add a top class centre-forward to his squad.
Despite the form of Fernando Torres, ‘The Special One’ is thought to see a new focal point to his attack as a key acquisition if the Blues are to mount a serious push for domestic and European glory.
As a result, he is ready to pay £35million to convince United to sell Rooney, who is entering the final 18 months of his contract.
The 28-year-old admitted over the summer that he was growing disillusioned with life with the Premier League champions, and could be tempted by a new challenge.
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