Brendan Rodgers is compiling a list of striker targets to replace Luis Suarez, should the wantaway Anfield forward leave the club this summer.
Yilmaz, a 27-year-old Turkey international, bagged 32 goals in 39 appearances for the Turkish giants last term, attracting interest from the likes of Arsenal, Chelsea and Real Madrid.
He's widely regarded to be one of the best orthodox strikers in European football, and Galatasaray's president Unal Aysal recently admitted the interest from the big European clubs could prompt a sale - for the right price.
"We have set a price for Burak Yilmaz," said Aysal. "We will only consider an offer which is in the best interests of the club and player.
"If Burak wants to leave and our transfer demands are matched, we could accept a deal."
His availability has reportedly piqued the interest of Liverpool, but they could face a battle to convince the Turkey international to join without the carrot of Champions League football.
Alongside Didier Drogba, Yilmaz helped Galatasaray to the Champions League quarter-finals last season, and they'll be hoping to go even further in next year's competition.
But with a potential windfall of £35m-plus for Suarez, Liverpool would be able to act decisively in the transfer market should they identify their ideal replacement for the Uruguayan international.