The former Arsenal and Liverpool midfielder is available after securing a release from his contract with Besiktas last week.
Oxlade-Chamberlain is keen to return to England and talks are now underway with Leeds.
Transfer expert Peter O'Rourke told Football Insider: "Oxlade-Chamberlain is available as well. A number of clubs have been having a look at him.
"He's got a great CV, played for Arsenal and Liverpool, he's a Champions League and Premier League winner from his time at Liverpool.
"Now that he's left Besiktas, clubs have been put on alert by his availability. There's interest from clubs in the Premier League, Championship and across Europe as well, with Leeds and Birmingham among them.
"So I'm sure he'd be ready to return to England after a couple of years away, and I expect there will be some movement on his future soon."