The 19-year-old joined Gladbach on a season-long loan and had struggled to make an impressing in the top tier of German football until this month, starting the Bundesliga outfit's last two league fixtures before the Christmas break.
The report claims that the two parties are locked in talks over the teenager's future, with negotiations progressing well after the Hammers decided to reduce the price tag on Oxford's head.
They had previously wanted around £7.1million for the versatile defender, who can play in both centre-back and holding midfield. Now, talks are said to progressing as the east Londoners want just £5.5million for their academy product.
Oxford first came to prominence as a 16-year-old, starting Slaven Bilic's first Premier League game in charge that saw him mark Mesut Ozil out of the game in a 2-0 win over Arsenal.
The youngster picked up the man of the match award as the Hammers earned a 2-0 win at the Emirates Stadium, and big things have been expected of Oxford since. But now it looks as though he will be playing his football in Germany.