Did Mehmet the Conqueror have the Iliad in his library?

Historians note that Mehmet the Conqueror knew Greek very well. We know that he had the handwritten copies of the Iliad from the Byzantian period brought to Topkapi Palace. In addition, it is also known that he had a very famous lithographer and author of the time, Johannes Dokeianos, prepare a copy of the Iliad for the palace library during his expedition to Lesbos, approximately ten years after he conquered Istanbul. For this reason, we cannot say that the palace historian Kristovulos' reports of what the Conqueror had said in Troy were flattery. Because Montaigne also mentions that Mehmet had found the hostile attitudes of the Italians odd in a letter that Mehmet the Conqeuror had written to Pope Pius II. The reason for this was that according to the Conqueror, Italians (referring to Virgil's Aenas epic) and the Turks came from a common root, meaning from the Trojans, and the Conqueror had taken revenge both for the Italians and for the blood of Hector that was spilled in Troy by conquering Constantinople.