The Arsenal midfielder is a man in demand as his contract has less than 12 months left to run at The Emirates.
A host of clubs from across Europe have registered an interest but the Gunners are keen for him to stay.
Manchester United, Manchester City and Liverpool have all approached Arsene Wenger about the 24-year-old.
Oxlade-Chamberlain is thought to want to remain in London and that is giving Chelsea confidence they can do a deal before the window closes this month.
That’s according to The Gambling Times who say AC Milan, Inter Milan, Monaco and Sevilla are also interested.
Chelsea are desperate for numbers and are actively trying to bolster their options before the August 31 deadline.
But Wenger has insisted this morning that he wants the former Southampton ace to stay.
He said: “I want him to stay here for a long time.
“I want him to be the English player in the next two years that a lot of people look at.”