The Blues are keen on the Gunners midfielder, who has just 12 months left on his contract.
Arsene Wenger is desperate to keep the player despite the potential of him leaving the club for nothing in 12 months time.
And Starsport understands Chelsea are ready to test Arsenal’s resolve by upping their offer for Oxlade-Chamberlain to £40m.
They’ve previously bid £35m for the England international, but that’s not got their London rivals interested.
Wenger wants to keep the player, but admits he can’t be 100 per cent sure no sale will go through.
“One hundred per cent never exists in our job,” the Arsenal boss said.
“I think all the three will stay. I will fight for them to stay.”
“After the board has to, of course, agree with me.
“And if they don’t agree we have to consider it as well, and I will accept it. But the board is behind me on that.”
Oxlade-Chamberlain is refusing to sign a new contract with Arsenal for anything less than £100,000-a-week.
