The 24-year-old favours a move to Merseyside, having set his sights on a regular run in his natural midfield role.
And according to widespread reports on Wednesday afternoon, the Reds have now approached Arsenal over a deal to bring the England international to Anfield.
The Times‘ Paul Joyce reports that the Gunners have told Oxlade-Chamberlain “he is no longer wanted,” and “want to offload him before tomorrow’s transfer deadline.”
The Reds are also pursuing a move for AS Monaco winger Thomas Lemar, however, with French outlet SFR Sport claiming the two clubs were meeting on Wednesday to discuss a big-money deal.
It was expected that it would be either Lemar or Oxlade-Chamberlain, but BBC Sport’s Ben Smith has now suggested it is “still possible” both could arrive on Merseyside this week.
The additions of Oxlade-Chamberlain and Lemar would significantly bolster Klopp’s options both in midfield and out wide.