Oxlade-Chamberlain is out of contract at the Emirates next summer.
The club have been keen on tie him down to new terms, with Arsene Wenger a big fan of the player.
But the Arsenal midfielder is refusing to sign a new deal.
The Sun report Oxlade-Chamberlain turned down a £180,000-a-week offer during talks with Gunners top brass yesterday.
Chief executive Ivan Gazidis reportedly got around a table with the England midfielder in a bid to thrash out his future.
But the Gunners head honcho was told by the player that he wants a move.
Chelsea are keen on the midfielder, and Starsport understands they'll bid £40m to get him.
Oxlade-Chamberlain could play Champions League football at Stamford Bridge this season, but Arsenal could hold on to him until next summer.
He'd be able to leave on a free, but boss Wenger is desperate to keep top talent at the club.
Mesut Ozil and Alexis Sanchez are two other players who could depart for nothing in 12 months time.