Oxford - who can play in defence or midfield - burst on to the scene at the start of last season, debuting as a 16-year-old against Arsenal and kept Mesut Ozil quiet in a victory over the Gunners.
The 17-year-old has a deal until 2018 at the London Stadium and the Hammers are keen for the youngster to sign a contract extension.
However, Oxford has stalled on signing a deal which has alerted the likes of United, City and Arsenal.
If the England U-19 international is to reject a new deal, West Ham are likely to want to sell given that they would rather cash in on the player, rather than taking it to a tribunal if he leaves at the end of his contract.