The west Londoners are ready to take advantage of Arsenal’s failure to tie the England midfielder down to a new deal.
Liverpool and Manchester City are already in the hunt with just a year left on Oxlade-Chamberlain’s contract.
Although he has had talks with Arsenal, he has yet to be made a former offer by Emirates chiefs.
Still only 23, Oxlade Chamberlain – signed from Southampton in 2011 – would add depth to Antonio Conte’s options at Stamford Bridge.
Last October the versatile star admitted he could leave in search of regular first-team football at another club.
He said at the time: “I do want to get more game time. There comes a time in your career where you have to re-evaluate things and think, “Is that going to be here or elsewhere?’.”
“I’m at a stage now where I definitely want to be playing and [so I am] pushing [the manager] to play me, getting feedback and if I’m not playing, finding out why I’m not playing.”
Will Alex Oxlade-Chamberlain be at Arsenal next season?
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