The Serie A club have been linked with the Brazilian for several months and the speculation has increased following the arrival of Roy Hodgson at Anfield.
Liverpool's new manager is expected to make changes to his squad and, with Emiliano Insua already the subject of talks with Fiorentina, Lucas could be one of the players who is sold to raise funds for reshaping.
Lucas was a regular in former boss Rafa Benitez's first XI last season after Xabi Alonso was sold to Real Madrid, but the 23-year-old still struggled to win over his critics.
Palermo, though, are admirers and sporting director Walter Sabatini has confirmed that they would like to sign the ex Gremio player, telling TGS: "We made a first offer to Liverpool for Lucas Pezzini (Leiva).
"But I deny that we have offered €6m. That is too much."