Oxlade-Chamberlain is in the final year of his contract at Arsenal.
Chelsea and Liverpool are keen on tempting him away from north London.
The Blues have launched a £35m bid to get him, and Oxlade-Chamberlain is interested in making the move.
Starsport understand Arsenal have made an offer to the England international and don't want to lose him this summer.
But their pitch falls short of his desired £120,000-a-week wage packet.
Gunners boss Arsene Wenger doesn't want to lose Oxlade-Chamberlain to a big domestic rival.
Speaking yesterday he hailed the midfielder, 23, as a huge star for the future.
“Personally, I think he is a hugely talented player,” said Wenger.
“He is on the way up and he will continue to move up because that potential is there.
“He is today very conscious of his qualities as well, which he was not always, and I personally believe he will be a very great player.”
Oxlade-Chamberlain has been at Arsenal since a 2011 switch from Southampton.
The Gunners paid £12m for him and within a year he was starting for England at Euro 2012.
Oxlade-Chamberlain has made 184 appearances for Arsenal in his six years with the club.
