The Blues are desperate to bolster their ranks before the transfer window closes with Antonio Conte keen on the England international.
Arsenal are expected to hold talks with Oxlade-Chamberlain this week after the winger turned down two new contract offers from the Gunners.
The Daily Mirror claim the 24-year-old has told Arsene Wenger face-to-face that he will not sign an agreement to stay at the Emirates.
And they also report Chelsea are confident of securing a deal for Oxlade-Chamberlain before the window shuts on August 31.
Arsenal are adamant they will not sell to their rivals with Alexis Sanchez also looking like he could leave for Manchester City.
The Chile superstar has also stalled on signing a new contract for the Gunners and is now in the last year of his current agreement.
Oxlade-Chamberlain has started both of Arsenal’s Premier League matches this season against Leicester and Stoke.
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And he will hope to feature for the Gunners on Sunday when they travel to Anfield to take on Liverpool.
Arsenal have not won the Premier League title since 2004 and will be in this year’s Europa League after finishing fifth last season.
Oxlade-Chamberlain impressed for the Gunners during the campaign, netting six times and providing 11 assists in all competitions.
Chelsea have already added Antonio Rudiger, Willy Caballero, Tiemoue Bakayoko and Alvaro Morata to their ranks this summer.
