The 28-year-old is about to enter the final 12 months of his contract with the Reds and has been widely expected to leave ahead of the 2022-23 season.
Oxlade-Chamberlain's time at Liverpool has been plagued by injuries, and he has struggled to become a consistent part of Jurgen Klopp's midfield ahead of Jordan Henderson, Naby Keita, Thiago Alcantara, James Milner and Curtis Jones.
Manchester United and Aston Villa have both been credited with an interest in the England international, with Liverpool initially slapping a £10m price tag on his head.
Liverpool were being tipped to sign a new midfielder in the current transfer window, but Real Madrid ultimately won the race for Aurelien Tchouameni, and Borussia Dortmund will not allow Jude Bellingham to depart just yet.
As a result, the Reds have supposedly put those plans on ice until 2023, and Oxlade-Chamberlain is still regarded as a 'valued member' of Klopp's first-team squad.
However, there are currently no updates regarding a potential contract extension for Oxlade-Chamberlain, who could still leave on a free transfer when his deal runs out in 2023.
The former Arsenal man registered three goals and three assists in 28 appearances for the Reds in all tournaments last term, with 17 of those games coming in the Premier League.
Oxlade-Chamberlain only started nine top-flight games in 2021-22, though, and he was left out of the matchday squad in seven of his side's last eight Premier League games.
Since making his £34.2m move from Arsenal in 2017, Oxlade-Chamberlain has registered 17 goals and 15 assists in 132 outings for Liverpool, winning the Champions League, Premier League, EFL Cup, FA Cup, Club World Cup and UEFA Super Cup in that time.
Liverpool are not expected to make a big-money midfielder signing before the current transfer window shuts, but they have already welcomed Fabio Carvalho to the club from Fulham.
The Reds are supposedly reluctant to loan Williams out again and will only sanction a permanent exit for the right-back, who helped Fulham achieve promotion to the top flight last term.