The 20-year-old is not in favour under Hammers boss Manuel Pellegrini with the centre-back having failed to make a single first-team appearance for the Chilean so far this season.
Oxford has stated that he is determined to stay and fight for his place in the side but Pellegrini has questioned whether the defender has the ability to make it into the first team.
The Gunners are believed to be keen to recruit the youngster in order to ease their own defensive crisis. With centre-half Rob Holding out for the season with a knee injury, manager Unai Emery wants to strengthen his options at the back and Oxford is seen as a potential solution.
The defender has made just 30 senior appearances in his career, 17 with West Ham and the other 13 whilst on loan spells with Reading and Borussia Monchengladbach. The German club reportedly tried to sign the centre-back on a permanent basis but their offer was knocked back by the Hammers.