The 16-year-old is attracting interest from several top Premier League sides.
The Red Devils had planned to make a move for the exciting 16-year-old in the summer, but Arsene Wenger wants to scupper United's plans by bringing him to the Emirates, claim the Mirror.
With two years left on his current contract at the Boleyn Ground, however, the Mirror state that Oxford is likely to cost £8million.
However, based on the brief glimpses of quality that the youngster has shown so far this season, that figure could well turn out to be a major bargain.
Although he has not played for the first-team since August, Slaven Bilic had enough confidence to hand him his Premier League debut away to Arsenal on the opening day of the season.
And he vindicated his selection by doing a sensational job in the holding midfield role. Oxford kept the Gunners quiet going forward, and forced Wenger to throw on a jaded Alexis Sanchez midway through the second-half. The Chilean was also unable to get the better of the youngster.
What made that performance at the Emirates all the more impressive was the fact that Oxford was playing out of position, as he is naturally a centre-back. It is therefore understandable why some of the Premier League elite are hoping to lure him away from the Hammers before his valuation shoots up further.