This is according to recent reports from The Daily Star, which suggest that all three of those aforementioned Premier League giants have been suitably impressed with the 15-year-old after he first burst onto the scene in the Hammers' youth set-up during the 2013/14 campaign.
Such a pursuit could prove tricky, however, with the same source claiming that West Ham are understandably keen to secure Oxford's long-term future with a new contract at Upton Park.
Oxford's rise to prominence has been remarkably swift, with the defender's good form for the club's Under 18 outfit rewarded with a place on the substitutes bench for Tuesday evening's Capital One Cup second round tie against League One promotion hopefuls Sheffield United - the first fixture between the two clubs since the unsavoury Carlos Tevez affair that saw the Blades awarded £20 million in compensation.
Although Oxford did not feature during the tense penalty-shootout win against Nigel Clough's side in East London, his involvement in the matchday squad will surely act as huge encouragement for the player moving forward.
Arsenal certainly appear to be in the market for new defensive recruits prior to Monday's transfer deadline, with Arsene Wenger evidently keen to provide further cover for the likes of Laurent Koscielny and Per Mertesacker at the Emirates Stadium.
While Oxford - if he were to make the short trip North - would obviously not be ready for regular first-team duties for some time, versatile Atletico Madrid outcast Toby Alderweireld could be the man to fill in in the short-term, with rumours on Wednesday claiming that Arsenal were edging ever closer to agreeing a deal for the Belgian international.
Manchester United's need for new defenders is particularly urgent, with Louis van Gaal currently persisting with an unconvincing back three of Tyler Blackett, Phil Jones and Chris Smalling.
The return of the experienced Jonny Evans to the fold for last night's clash with MK Dons was supposed to provide a certain amount of relief, although Van Gaal will surely not have been at all impressed with the Northern Irishman's showing during the quite unbelievable 4-0 rout in Buckinghamshire.
Chelsea, meanwhile, can lay claim to last season's meanest backline, with the established partnership of John Terry and Gary Cahill helping to ensure that the Blues conceded just 27 goals in 2013/14 - a mark that was 10 fewer than eventual champions Manchester City.
Oxford could certainly appeal to Jose Mourinho as a talented option for the future, with January's capture of 19-year-old Kurt Zouma indicating that he is already beginning to plan for life post-Terry.