The Daily Mirror is reporting that both the Gunners and Everton are seriously interested in a move to sign the 20-year-old defender from the Hammers.
The same story claims that Arsenal manager Unai Emery is “desperate” to bolster his options at the back ahead of the second half of the season.
The article also suggests that West Ham may be willing to sell Oxford after Manuel Pellegrini hinted that he may not have a future at the club.
The same report says that Manchester United were also keen on a move for Oxford before he signed a new long-term contract with West Ham.
The young defender has not made a senior appearance for West Ham United so far this season.
Meanwhile, Arsenal are likely to be linked with a number of players in the coming weeks as the Gunners ponder the chance to strengthen their options at the back.
The north London side will return to Premier League action on Saturday when they travel to Anfield to take on Liverpool FC.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news