Oxford played for West Ham in their match against Crystal Palace, but he is thought to still be seeking a move elsewhere.
The youngster was set to join Borussia Monchengladbach on loan, for the second time this season, but that deal is now in doubt.
A series of injuries have struck at West Ham, and David Moyes may now be forced to keep the prospect around.
Oxford reportedly would rather move elsewhere, as he feels his development would be best served by a move away.
If Oxford does stay at West Ham, he will likely be used as a covering option.
The Hammers are set to be without Pedro Obiang for the remainder of the season, and if Moyes lets Oxford go now, without signing any cover, he could be left short of options for the remainder of the campaign.