West Ham leased midfielder Jesse Lingard for £1.5m and was keen to acquire the right to buy the player for £15m, but Manchester United refused, deciding that the midfielder could rise in value if he performs well for the Londoners.
Eurosport claims that the 28-year-old Englishman could leave Manchester United in the summer.
The Manchester club will now be charging over £20m for Lingard if they decide to sell him.
It is possible that Lingard could be included in the transfer of midfielder Declan Rice, for whom West Ham will demand at least £50m.
Lingard has scored three goals and given one goal in five EPL games for West Ham.