Bilic told Hürriyet reporter İzzet Çapa: “There is a striker problem right now at West Ham and if the board agree to sign a forward Burak Yilmaz is on my transfer list.”
The Hammers boss went onto praise Yilmaz and also underlined that he only has a few names on his current list.
“Burak is a great player he could play at any top club in the world and as for my list there isn’t 15-20 players there is just a few names,” he added.
Çapa went onto tell his readers not to be surprised if Yilmaz ends up in England by the end of the winter transfer window.
Bilic had plenty of time to familiarise himself with the Galatasaray striker over the two seasons he spent in charge of Beşiktaş.
The current West Ham boss loss all four games against the Lions side during his time in the Turkish Super League.
Yilmaz has won two league titles scoring 81 goals in 140 games for the Lions since joining from Trabzonspor in 2012.
The 30-year-old striker has another three-years remaining on his current contract and earns €2.85 million per-season – excluding bonuses.
Galatasaray had rejected previous offers made for Yilmaz over the summer but could be forced to consider any January offers made as the club has fallen into trouble with UEFA over failing to meet Financial Fair Play regulations.
The CFCB adjudicatory chamber will reach a final decision regarding Galatasaray’s punishment for failing to meet FFP regulations by the end of February.
UEFA said in an official statement: “The Turkish club Galatasaray has failed to comply with the break-even requirement during the monitoring period assessed in the 2015-16 season. The CFCB [Club Financial Control Body] adjudicatory chamber will take a decision and communicate it by the end of February.”