An old bath house was being restored. Because of its proximity I conclude its is part of the külliye of the Yalinayak Mosque. From another website I understand its builder was Hasan Cavus, who was one of the sergeants of the court council and who gave the news to Sehzade Selim that Suleiman the Magnificent was dead in Zigetvar.
Also it is stated some claim the mosque to be by the famous architect Sinan, but there is no proof. However, then it will be from the 16th century.
Another website states: One of the most significant structures of the kulliye is the Yalinayak bath. Both the men’s and women’s part of the bath has a rich lighting.
I think I agree, and hope to return someday.