The Daily Express says Blues want a deal wrapped up by August 26.
Chelsea have had two bids turned down but are readying another offer of around £28million plus add-ons to submit this week.
Rooney, who missed most of United’s pre-season preparations but played 67 minutes of England’s friendly win over Scotland on Wednesday, has told new United boss David Moyes he wants to leave.
United remain adamant the striker is not for sale but Chelsea are still confident they can do a deal because of Rooney’s desire to go to Stamford Bridge.
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