The Independent claims that both clubs are interested in signing the England under-19 international who made seven Premier League appearances for West Ham last season.
Oxford came to the attention of the wider footballing public by starring for the Hammers in their 2-0 victory over Arsenal at the Emirates last season.
The England under-19 international has one year remaining on his contract with the East London club, and despite West Ham’s determination to keep hold of one of their brightest young talents, the fact that he could leave for a compensation fee once his deal expires next summer, could see them open to offers.
It is thought that Pep Guardiola’s City are currently leading the race to sign Oxford, having made an official enquiry as to his availability via telephone on Monday.
But United have scouted the player several times, and new manager José Mourinho is a known admirer of the Edmonton-born youngster, so the Red Devils will likely try to entice him to the red half of Manchester.
Despite his tender years, Oxford has a level of maturity to his game which would be befitting of a much more experienced player. His physical robustness — standing at 6ft 3in — and ability to play at centre-back or as a defensive midfielder, has marked the young man out as one of the hottest prospects in English football.