Per the source, the Lions are in pursuit of a new central midfielder as they have still not sufficiently filled the void left by the departure of Felipe Melo.
The Brazilian midfielder joined Inter on transfer deadline day last summer and the Lions have failed to find a replacement.
Galatasaray are prepared to loan Lucas or pay a €3 million upfront fee to sign him on a permanent deal.
Lucas could however, be out injured which would put the Lions efforts to sign him on hold.
The experienced midfielder suffered an injury in the 2-0 victory over Huddersfield last night according to the Daily Star.
The severity of Lucas’ injury is still unknown and the Reds will have to wait for the results of his tests to find out how long he will be out.
Galatasaray could however, face competition from Besiktas who have also been closely linked with Lucas over the past season.
The Black Eagles were close to signing Lucas last season but Brendan Rodgers vetoed the loan move.