Moreno's Liverpool deal expires at the end of the season and could leave the club on a free transfer in the summer.
Sources have said Liverpool offered Moreno a long-term contract at the end of last season before the player's camp then responded with a counter-offer.
Having been unable to settle on terms, Liverpool and Moreno's representatives agreed to hold further talks before the end 2018.
However, sources have said these are yet to take place, and Moreno is now weighing up his options as he desires regular game-time at the age of 26.
Behind Andrew Robertson in the left-back pecking order at Anfield, Moreno has been restricted to just 90 minutes of action so far this season.
Sources have said that at least two La Liga clubs are interested in Moreno, with the player permitted to hold discussions with teams outside the Premier League from January.
Meanwhile, Moreno's potential departure could benefit Liverpool's young left-back Adam Lewis, who signed a professional contract last December.
The 18-year-old is highly thought of at the club's Kirkby academy and trained at Melwood with the first team over the international break.