Arsenal want to keep Oxlade-Chamberlain, who will be out of contract next summer, but have struggled to meet his wage demands. That has led to Chelsea emerging as an interested party, hoping to take advantage of the situation.
Chelsea are thought to need to pay a fee of around £35 million to convince Arsenal into a sale as they face the prospect of losing the England international for free next summer.
If the 23-year-old midfielder's wage demands are met, he would more than double his salary from his current £65,000-a-week, to become one of Chelsea's highest-paid players. The wage demands may come down as negotiations remain ongoing.
Chelsea are in urgent need of new signings after seeing both Cesc Fabregas and Gary Cahill sent off in the opening day defeat to Burnley at Stamford Bridge at the weekend.
Oxlade-Chamberlain is a central midfielder but last season he was used by Arsene Wenger as a wing-back on both the left and right sides.
Danny Drinkwater, Ross Barkley and Virgil van Dijk are among the club's other targets, but Juventus are continuing to resist any sale for Alex Sandro, even for a fee of around £65m.