Per the source, Galatasaray must keep within budget as they remain under FFP investigation and want to reduce spending.
The Reds are reported to be keen on parting ways with Lucas and Galatasaray are prepared to offer a three-year deal worth €2.4 million per-season.
Alternatively the Lions are prepared to loan Lucas with a buyout clause option agreement with Liverpool.
Galatasaray remain keen on signing the Brazilian midfielder despite his recent hamstring strain that will rule him out for the next month.
The Lions have made signing Lucas a priority over the summer but will not be able to offer the 29-year-old European football next season.
The Istanbul giants are currently banned from European competition due to failing to meet FFP regulations.
Galatasaray had a poor league campaign last season but still managed to win the Turkish Cup beating arch rivals Fenerbahce in the final.