The former England international, who has seen his stint on Merseyside being plagued with injuries, is out of contract at Anfield in the summer.
Oxlade-Chamberlain has no lack of suitors with a number of Premier League clubs showing interest in signing him either in January or in the summer.
However, Brighton are not among those trying to convince the player to choose a move to the Amex.
Brighton have their sights set on Ukrainian defender Mykola Matviyenko, who is currently manager Roberto De Zerbi’s priority transfer market for January.
Oxlaide-Chamberlain could be looking to hold out until the summer before leaving Liverpool wherein he could bank a significant signing-on fee.
However, he might find his chances limited then considering the huge pool of players clubs will have the option to choose from.
The 29-year-old has been with Liverpool since 2017 and has featured in 143 games for Jurgen Klopp’s side making 33 goal contributions.