The Reds were linked with experienced Brazilian international Alves earlier in the summer transfer window, although manager Brendan Rodgers eventually turned to promising Spanish duo Alberto Moreno and Javi Manquillo to bolster his full-back options ahead of the new Premier League season.
However, according to the latest speculation from The Daily Star - which carries quotes from Barcelona boss Luis Enrique confirming the arrangement for Alves to leave - Liverpool could revive their pursuit next summer with the 31-year-old available on a free transfer following the expiration of his current contract.
Alves is one of Barcelona's longest serving senior first-team players, having moved to the club from La Liga rivals Sevilla back in 2008.
In his six-year stint with Blaugrana, the energetic right-back has won four domestic titles, two Copa del Reys and two Champions League winners medals along with a plethora of other slightly less prestigious silverware.
He made 27 appearances during Gerardo Martino's final season in charge at Barcelona, and was also believed to be being pursued by both Paris Saint-Germain and Inter Milan during recent months.
A good move for Liverpool?
While his exit from Barcelona now appears certain, would Alves represent a positive piece of business for Liverpool one year from now?
After all of the madness that accompanied yesterday's deadline day proceedings it feels bizarre to already be contemplating next year's window, yet there could be some merit to Rodgers bringing in such an experienced campaigner.
England's Glenn Johnson - who missed Sunday's 3-0 win over Tottenham at White Hart Lane with a thigh injury sustained during the disappointing loss to Manchester City - has been far from convincing at Anfield, with Rodgers' deal for Manquillo reflecting the need to provide him with adequate competition.
Ultimately, whether or not Liverpool do once again chase the signature of Alves may just depend on how well Manquillo adapts to life in England.
With his loan spell at Anfield from Atletico Madrid set to last for two years with the possibility of a permanent transfer on the horizon, it could be that he is simply not needed on Merseyside.
Liverpool fans, how would you feel if your club did move to sign Alves on a free transfer in 2015? Would he represent an upgrade, or do you feel comfortable with Johnson and Manquillo at right-back? Leave us your thoughts in the comment box provided below.