Oxlade-Chamberlain, 23, has just 12 months remaining on his contract at the Emirates and has grown frustrated with his bit-part role at the club.
He started just 16 Premier League games last season and is apparently considering a move elsewhere in a bid to secure regular minutes.
Liverpool boss Jurgen Klopp is an admirer of the England international as he bids to bring in more attacking flair and pace to Anfield.
He has already completed the £39m signing of Mohamed Salah from Roma and the Daily Mirror claim he has now set his sights on Oxlade-Chamberlain.
The former Southampton man has apparently grown frustrated at the lack of talks over new deal at Arsenal.
And the German boss is ready to swoop with a £30m bid being prepared for the winger.
The Mirror say the chances of the transfer going through are increasing as Klopp looks to build a squad capable of coping with the dual demands of the Premier League and possible Champions League campaign next season.
The prospect of Champions League football next season could be the deal clincher.
And Liverpool will discover their fate in August when they contest a play-off match with the winners progressing to the group stages.
Klopp is also looking to bolster his defensive ranks and a move for Southampton star Virgil Van Dijk could be back on.
The Dutch international still harbours ambitions of playing football despite the Reds publicly apologising for an alleged illegal approach.
