The Reds are looking for quality competition for current number one Simon Mignolet, having failed in a summer move for Aston Villa stopper Shay Given.
Brendan Rodgers allowed Pepe Reina to leave the club for Napoli on loan after landing Mignolet from Sunderland in a £9 million deal.
Rafael Benitez, who is currently in charge of the Serie A club, expressed his surprise at the Reds’ decision to allow Reina to leave, and his departure has left the Anfield outfit desperately short of quality cover for the big Belgian.
Australian Brad Jones is the only other goalkeeper named in the Reds’ Premier League squad list, and Adan has now emerged as a target.
The Spaniard rescinded his contract with Real Madrid on transfer deadline day, and is currently on the lookout for a new club.
Rodgers has long admired the 26-year-old, and could now swoop in with a contract offer.
However, Adan may yet choose to further his career elsewhere after playing second fiddle to Iker Casillas for three years.
A number of La Liga clubs are believed to be monitoring his situation, and it is understood he would rather remain in Spain than move abroad.
That is unlikely to deter Rodgers, though, who is desperate to recruit a ‘keeper before the January transfer window.
Should he fail in his bid to land Adan, he may look to the emergency loan market – which opens on 10 September – before looking to bring in a stopper permanently in the next transfer window.