Per the source, the Serie A outfit have been keeping tabs on the Brazilian midfielder and are ready to make a move.
Lucas is currently the most experienced member of the Liverpool squad having made 315 appearances for the Reds over the course of nine seasons ever since joining from Brazilian giants Gremio.
The 29-year-old does however, face an uncertain future at Liverpool following a string of summer midfield signings.
Galatasaray sporting director Levent Nazifoglu revealed that Lucas was on the verge of joining the club until Liverpool pulled the plug on the deal.
“We are no longer pursuing Lucas Leiva, we will continue efforts to sign alternative names instead,” Nazifoglu was quoted as saying by Turkish-football.com.
Istanbul rivals Besiktas have also been linked with the experienced midfielder as they continue efforts to strengthen their midfield going into the Champions League group stages.
Lucas is currently recovering from a hamstring strain and missed the Reds first Premier League game of the season as a result.
Liverpool beat Arsenal 4-3 at the Emirates but even if he was fit he would have been unlikely to play.