Oxford has been on the books of West Ham since 2011 and has a contract until June 2019.
According to the report, the uncertainty over who the United first-team manager next season will be is the reason why the Red Devils could miss out on the 17-year-old, who can play as a central defender or as a defensive midfielder.
The Mirror claims that delaying a decision over the future of manager Louis van Gaal has put signing of new players on hold, including that of Oxford from West Ham.
“Oxford wants his future sorted before he reports for England Under-19 duty next week,” adds the report. “The Young Lions are travelling to South America for a double header against Mexico as they step up their preparations for next month’s Euros in Germany.
“Oxford would welcome the chance to work with Van Gaal because of the Dutchman’s willingness to put his trust in young players.”
The Mirror has also reported that Premier League giants Manchester City are interested in the teenager as well.
Oxford made seven appearances in the Premier League for West Ham this past season. The teenager had a pass accuracy of 84%, and won three headers and five tackles.