Reds boss Brendan Rodgers is drawing up a shortlist of targets to replace Luis Suarez, should the unsettled Uruguayan secure a move away from Anfield this summer.
The likes of Real Madrid, Chelsea and Arsenal have been credited with an interest in Suarez and should he leave Liverpool, Rodgers will be keen to bring in a big-name signing to help fill the void.
Yilmaz is regarded as one the best strikers in Europe after impressing for Galatasaray in the UEFA Champions League last season and the Turkish international is thought to be on Rodgers' radar.
The 27-year-old scored 32 goals in 39 appearances for Galatasaray last season after arriving from Trabzonspor
Galatasaray president Unal Aysal recently admitted they would be prepared to sell Yilmaz for the right price this summer.
"We have set a price for Burak Yilmaz. We will only consider an offer which is in the best interests of the club and player," admitted Aysal.
"If Burak wants to leave and our transfer demands are matched, we could accept a deal."