The Times reports that United plan to make a £10million bid for the Everton and England left-back.
Everton had been hoping for around double that sum, but they are ready to sell as Baines is desperate for a move to Old Trafford.
United boss Sir Alex Ferguson has long been linked with a move for the England international defender.
Fergie is keen to bring in Baines as a long-term successor to Patrice Evra.
Baines has three more years left on his current contract with the Toffees.