The 15-year old central defender has been earmarked for future success, appearing for the Hammers' under-18 team, as well training with Sam Allardyce's first-team squad and receiving three caps for the England Under-16 national side.
Standing at 6ft 3ins gives him an advantage over others in his age group, but many pinpoint his ball-playing skills as his finest trait - an important ability for those linked with Arsenal.
Speaking last October to the official West Ham website, under-18's assistant manager Mark Phillips lauded Oxford following his call-up to the international side.
Phillips said: "Reece has been with the Club since the U9s.
"In all fairness to Reece, and he'd probably admit this himself, he is really on an upward curve. In the last year, he has really come up and is at the top of his game.
"They [Oxford and first-year scholar Kyle Knoyle] are both good users of the ball and Reece, with his height, is quite dominant in the air in both penalty boxes and he gets his fair share of goals. It's good for the Academy as a whole that they have been called-up.
"When you ask people about West Ham, they tend to talk about flair midfield players and people who pass the ball, but we are producing good defenders and we did, of course, produce Bobby Moore!"
To be so highly thought of at such a young age can always be a burden, although Phillips believes the striker-turned-defender can still vastly improve.
"Reece came into the Club three years ago when he joined the U13s. He originally came into the Club as a centre forward and probably had about two or three months there before one of the coaches suggested he move to centre-back, and he hasn't looked back from there.
"He has learnt the position, has a thirst for knowledge and is excellent in both boxes and has got a good passing range. I think there is a lot of growth in him as a player as he has only been in the Academy for three years.
West Ham are determined to retain their starlet, knowing that they can offer Premier League first-team opportunities to the player - a key component for youth development. However, Arsenal are world renowned for their youth improvement, having brought through the likes of Cesc Fabregas, Seb Larsson and Jack Wilshere - all established internationals.
Any young player could sense their career would follow a sharp upward trajectory if they were to sign for Arsenal, and the Daily Mail is reporting that the Gunners are doing all they can to convince Oxford to join on academy terms - before agreeing a professional deal when he turns 17.
The report suggests that a deal could be agreed that automatically turns into a full-time deal on his 17th birthday - meaning other clubs could not steal him off the Gunners for a cut-price youth fee.