The Premier League leaders have an impressive strikeforce at present, but may yet want to add to those options.
Yilmaz has plenty of European suitors at present.
The likes of Bundesliga clubs RB Leipzig and Eintracht Frankfurt want to buy him, along with the Reds.
Nottingham Forest have also shown an interest in the striker who has already scored four goals this term.
"We have 20 percent of Baris Alper Yilmaz's share but Galatasaray has not requested a meeting with us on this issue," Keciorengucu president, Sedat Tahiroglu told Turkish news outlet Aksam.
"I hear Liverpool and Arsenal want him but I know Nuri Sahin definitely wants him (at Dortmund).
"I don't think the price will be €50 million (£42 million). He can be sold for around €30 million (£25 million). The path needs to be paved for young people for Turkish football. Hopefully, he will make the decision that is good for him.
"The money is not important. The important thing is for Baris Alper to go to a team where he will be successful because he will be the face of Turkey."