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The England international has spent the past three years on the Gunners’ books since moving to the Emirates from Southampton.
And during that time he’s racked up 59 first-team appearances, as well as helping Arsene Wenger’s men beat Manchester City to the 2014 Community Shield.
Chambers enjoyed a loan stint under Aitor Karanka and Steve Agnew at Middlesbrough last season but was not able to help them stave off relegation.
Reports suggest the 22-year-old’s return to Arsenal this summer could prove short-lived, with Frank De Boer keen to take him to Selhurst Park.
Last week The Telegraph claimed Palace had offered around £16m for Chambers.
The Mirror have now picked up the story and say negotiations are ongoing.
They reckon Arsenal are holding out for £20m before they’ll sell Chambers.
Whether new Palace boss De Boer will be prepared to pay that much remains to be seen.
But it’s clear the Dutchman’s building from the back ahead of the upcoming campaign.
De Boer signed the versatile Jairo Riedewald from Ajax yesterday and is interested in Liverpool outcast Mamadou Sakho too.