The Red Devils will increase the player's wages from £70,000-a-week to £100,000-a-week, which would cost them £20 million.
It is thought that handing such high wages to the left-back in addition to Wayne Rooney's reported £65m deal would send out a warning to Manchester City that United are capable of spending big money when necessary.
Barcelona and Real Madrid were previously reported to have been interested in acquiring the services of the Frenchman, but a four-year contract may turn their heads in another direction.
Evra's current contract at United runs out in 2012.
Evra his slipped 33 places in the latest edition of the Castrol Rankings and is now rated as the 182nd best player currently plying his trade in one of the top five leagues in Europe.
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