Per the source, the Lions have made Liverpool a €3 million offer for the Brazilian midfielder but want Lucas to lower his wage demands.
Galatasaray are currently under FFP investigation after being banned from European competitions for a season.
Despite the ban and financial problems Galatasaray are still among the top 30 clubs in the world in terms of revenue according to Deloitte.
The issue Galatasaray have had is uncontrolled spending and that his something the new board have made a priority to change.
Lucas would have to accept a lower wage packet if Galatasaray were to complete his transfer.
Galatasaray could however, face competition from Istanbul rivals Besiktas who have also been closely linked with move for the experienced midfielder.
Liverpool boss Jurgen Klopp has advised Lucas as well as several other players to leave the club over the summer according to the Mirror.
Per the source, Klopp has advised Lucas, Cristian Benteke, Adam Bogdan, Tiago Llori, Mario Balotelli and Lazar Markovic to leave.