The former West Ham United shot-stopper spent another season as Alisson Becker and Caoimhin Kelleher's backup in 2023-24, where he did not make a single competitive appearance.
Adrian has played just 26 times for the Merseyside giants since arriving in the summer of 2019, keeping seven clean sheets, and his most recent outing came in the 2022 Community Shield success over Manchester City.
The 37-year-old's contract expires at the end of the month, but Liverpool confirmed that they were in talks with the goalkeeper over a new deal, having agreed a short-term extension with him last summer.
However, Adrian had already outlined his desire to return to Spain with Real Betis, whom he represented for 15 years from 1998 to 2013 before joining West Ham United on a free transfer.
Adrian 'on brink' of Real Betis return
According to the Daily Mail, the Spaniard has decided not to sign the new deal he was offered by Liverpool and is now on the cusp of making his Real Betis comeback 11 years after his departure.
Adrian turned out 32 times for the Betis senior team prior to his move to West Ham, where he kept 43 clean sheets in 150 matches during a successful spell and left after six seasons to join Liverpool on a free.
The goalkeeper departs Anfield having won the Premier League, Club World Cup, FA Cup, two EFL Cups, the Community Shield and the UEFA Super Cup, and he made 11 top-flight appearances for the Reds in the 2019-20 campaign.
Adrian could be one of two shot-stoppers to head for the Anfield exit door before the summer is up, as number two Kelleher is also pining for regular first-team football after excelling in Alisson's absence last season.
The Republic of Ireland international is understood to be on the radar of Nottingham Forest and has also been linked with a move to Celtic, who are in the market for a replacement for the retired Joe Hart.
However, Liverpool apparently knocked back an approach from Forest in January and are after £35m to let Kelleher depart, but they will not stand in his way if the right offer comes in.
Which goalkeepers could Liverpool target this summer?
Adrian's departure will already hasten Liverpool's need to enter the goalkeeping market, while Kelleher leaving would surely lead to Arne Slot earmarking that position as a priority for his first summe window.
A reunion with Feyenoord shot-stopper Justin Bijlow has been mooted, but Arsenal - who will likely lose Aaron Ramsdale in the coming weeks - will rival the Reds for his signature.
Sunderland's Anthony Patterson and Athletico Paranaense's Bento have also been linked with moves to Liverpool, who supposedly tried and failed to hijack Juventus' move for Monza's Michele Di Gregorio.