Liverpool have offered Adrian a new contract as their Premier League retained list confirmed the departure of several Academy players.
Adrian will become a free agent at the end of the month but has been in talks over extending his Anfield stay into a fifth season having arrived in August 2019.
The Reds had previously announced the exits of Roberto Firmino, James Milner, Alex Oxlade-Chamberlain and Naby Keita after their contracts expire. Milner has already agreed to join Brighton, Keita has moved to Bundesliga side Werder Bremen while Oxlade-Chamberlain is receiving strong interest from Aston Villa.