With the 24-year-old having less than a year remaining on his contract, the likes of Chelsea and Liverpool have been linked with his signature before the end of the transfer window.
Arsenal want to keep a player who has been part of their first-team squad since 2011, with manager Arsene Wenger acknowledging that the former Southampton trainee is a key part of the club's plans for this season and beyond.
However, according to The Telegraph, Chelsea are confident of securing Oxlade-Chamberlain's signature within the next seven days as Antonio Conte looks to strengthen his squad at Stamford Bridge.
It has been suggested that the versatile England international has been offered wages of £180,000 per week to remain at the Emirates Stadium, but those terms are likely to be rejected.
Oxlade-Chamberlain has made 197 appearances for the Gunners, but only 67 of those outings have been starts in the Premier League.