The paper said Mata had agreed personal terms with the English champions and will undergo a medical on Thursday.
The Spain international has been linked with a move away from Stamford Bridge after struggling to cement a regular starting spot under manager Jose Mourinho.
The 25-year-old has found game time hard to come by this season, with Mourinho favouring Brazil internationals Oscar and Willian and Belgium's Eden Hazard.
United manager David Moyes is looking for reinforcements to bolster his squad's creativity after a poor start to the season left them seventh in the Premier League and 14 points adrift of leaders Arsenal.
The fee would break United's transfer record paid for striker Dimitar Berbatov, who joined in 2008 from Tottenham Hotspur for 30.75 million pounds.
Mourinho has consistently maintained that Mata still has a role to play at Chelsea, but his determination to keep hold of the player is now likely to be tested.
Chelsea paid 23.5 million pounds to sign Mata from Valencia in 2011 and he has been voted the London club's player of the year two seasons in a row.
(Reporting by Toby Davis; editing by Ed Osmond)
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