Oxford is the Hammers’ prized prospect, and the likes of Manchester City, Chelsea and Liverpool are all said to be tracking the England youth international.
However, West Ham are understood to be determined to keep hold of the 17-year-old and would rather he left temporarily than permanently.
Oxford is keen to get first team football, but Slaven Bilic has been cautious with utilising the youngster.
The Croatian boss has played the academy graduate in eight matches this season, with his performance against Arsenal being particularly memorable.
Fulham are hopeful of agreeing a deal for Oxford, though, as they feel they could give him regular action.