Oxford joined Gladbach on a season-long loan deal in the summer, but has struggled to make an impact when making just one appearance in the Bundesliga.
That came last month when he was a late substitute during a 3-1 win at Hoffenheim, but sporting director Max Eberl says a permanent deal could still happen.
Much will depend on West Ham although as far as Eberl is concerned, Gladbach want him.
"He's a top lad," Eberl told German the Rheinische Post. "He's come on well and we're very happy with him. It takes time to find your feet in the Bundesliga, but we certainly want him to stay. West Ham now have the final say.”
When quizzed about his lack of action, Eberl added: "We could look into signing him anyway. When our injured players are back, we're going to have quite a strong troop."