The 19-year-old is under contract at the London Stadium until 2020, but has had few first-team opportunities of late and spent last season on loan at Borussia Monchengladbach.
West Ham have also made nine first-team signings during the summer transfer window, which would likely see Oxford slip further down the pecking order.
Although Oxford has been linked with a return to the Bundesliga, Sky Sports News suggests that the centre-back has penned a new deal with the East London club.
In addition, "sources close to the player" claim that Oxford considers himself an "Iron" through and through, and is determined to do everything in his power to help the club if selected.
Oxford has made 17 first-team appearances for the Hammers.