The Daily Mirror is reporting that the Reds are keeping tabs on the Argentina international ahead of the summer transfer window.
Liverpool FC have funds to invest in a new attacking midfielder to replace Philippe Coutinho in a £142m move to FC Barcelona in January.
The same article states that Lanzini could have a decision to make if Reds boss Jurgen Klopp decides to step up his interest in the Argentinian forward.
According to the same report, the 25-year-old is an alternative to Lyon playmaker Nabil Fekir, who has also been linked with a move to the Anfield outfit.
Lanzini has scored five goals and has made six assists in 27 appearances in the Premier League last season.
Liverpool FC finished in fourth place in the Premier League table last term after the Reds managed to see off competition from Chelsea FC for the final Champions League qualification spot.
The Merseyside outfit will take on current holders Real Madrid in the Champions League final in Kiev.
Liverpool FC signed Netherlands international Virgil van Dijk in a £75m deal from Southampton in the January transfer window.
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