The England global had a very positive end to the season and looked like a new player after being deployed as a right-wing-back once Wenger shifted to a three-at-the-back system, and this will have undoubtedly raised his stock as it seemed as though he was struggling to fit in previously.
The youngster's contract runs out in 2018 and if the Gunners do not extend his contract, they risk losing him for free next season.
But Oxlade-Chamberlain has just one year remaining on his current contract at the Emirates and the Mirror claim that while talks have taken place over an extension, he's yet to be formally offered a new deal by the Gunners. The fee was set to rise to £15m after including add-ons.
The Italian relied quite heavily on the wing-back pairing of Victor Moses and Marcos Alonso last term, and was able to lift the Premier League trophy on the first time of asking due to the success the players produced in the role. His injuries have also not helped but Oxlade-Chamberlain has made a number of substitute appearances or does not last the 90 minutes often when he does start games.
"I personally think it's vital that Chamberlain stays at Arsenal", Wenger said in April.
Liverpool are looking for more depth in their attacking options and Oxlade-Chamberlain also has the kind of versatility that could make him a very attractive option to Jurgen Klopp.
Wenger has previously suggested he is keen to agree a longer deal for the 23-year old, whose contract runs out next year.