The Anfield side were linked with Neves, who has been capped twice by Portugal, during the summer but it is thought Porto snubbed their advances.
However, Italy’s Calciomercato claim Liverpool have retained an interest and have again made contact with his representatives, with Juventus and Chelsea also believed to be weighing up moves.
Neves is under contract until 2019 so Porto are under no pressure to sell but it is understood that he has a 40million euros release clause.
If Liverpool do decide to make a move they may well wait until the summer rather than swoop in January, as Porto would be more open to a sale if it becomes clear Neves does not intend to sign a contract extension.
Jurgen Klopp feels Liverpool are ready to make the final step of their 'very exciting journey' by beating Real Madrid on Saturday.
Alphonse Areola has emerged as a possible transfer target for Napoli amid claims he wants out of PSG with Gianluigi Buffon set to join.