Oxford joined the Hammers in 2011 from Tottenham Hotspurs academy and made his first-team debut for the east London club three years later.
But the 20-year-old has been unable to establish himself as a first-team regular, spending the last year in Germany with Borussia Monchengladbach.
West Ham are ready to sell Oxford this month and Monchengladbach are believed to be keen to secure his signature permanently.
But the Daily Mirror say Oxford, who has represented England at youth level, would rather stay in England and has his heart set on a move to Arsenal.
Unai Emery is desperate to strengthen his defensive options at the Emirates and Oxford is one of a number of defenders to be linked with the Gunners.
But Emery has limited funds to work with this month and may have to wait until the summer to bolster his squad.
Oxford, the Daily Mirror say, is keen to delay a move from West Ham to potentially join the Gunners at the end of the season.
West Ham are ready to sell Oxford for around £3million but a number of other English clubs are also monitoring his situation, with Everton believed to be admirers.
Arsenal looked into signing the versatile youngster before he penned his last contract at West Ham, who are currently tenth in the Premier League table.