The 19-year-old joined Monchengladbach for the entirety of the 2017-18 season in June and has made four appearances for the club in all competitions thus far.
Despite getting little game time, the Foals are believed to view Oxford as an exciting prospect for the future and are eager to recruit him permanently.
On Thursday, Leipzig reportedly stepped in with an offer of £8m for the versatile player, which could potentially rise to nearly £17m.
According to Sky Sports News, however, West Ham are likely to recall Oxford in January so as to be utilised by new manager David Moyes in the team's Premier League survival battle.
The England Under-20 international signed a new Hammers contract last year that tied him to the club until 2021.