The report claims that the Brazilian international could be on the verge of an exit from Liverpool as part of head coach Jurgen Klopp’s overhaul of the squad.
Lucas’ future at the club is reported to be in doubt after a nine year spell at Anfield.
Besiktas almost signed Lucas on loan last summer but former manager Brendan Rodgers pulled out of the most at the last minute.
The Black Eagles are back in the market for a central midfielder in preparation for their Champions League campaign next season.
Besiktas are already stretched in central midfield and could be set to lose experienced central midfielder Atiba Hutchinson over the summer.
The Istanbul giants have made strengthening their central midfield a priority over the summer and have also been linked with Chelsea midfielder Mikel.
The Eagles won the league title last season and booked a spot in the Champions League group stages as a result.