The defensive midfielder was signed by Rafa Benitez back in 2007 and has spent nine seasons at Liverpool.
Lucas failed to establish himself as a first team regular under Klopp last season and the arrival of Grujic was damaged his chances further.
It is understood that the midfielder has already agreed personal terms with the Turkish outfit Galatasaray and will join them this summer.
Apparently Lucas Leiva has accepted a deal worth 2.5 million Euros per-season deal with Galatasaray and the Turkish side have offered Liverpool a fee of around 3 million Euros.
It remains to be seen if Liverpool will accept the offer now.