Britain has backed Turkey's bid to join the EU and Nick Baird, the British ambassador to Turkey, said the queen would highlight that support.
Turkey began EU membership talks in 2005, but progress has been slow over disagreements on divided Cyprus and opposition from some European countries.
Baird said: "It is obviously a difficult time. But the message is that we just have to stay resilient, we just have to keep going.''
On Tuesday evening, the queen will attend a banquet hosted by Abdullah Gul, Turkey’s president.
Gul is a member of the ruling AK party, which is an Islamic-rooted organisation.
His wife, Hayrunnisa, is likely to wear a headscarf at the banquet, despite a ban on them in public and governmental buildings.
The Queen will also visit Istanbul and the western city of Bursa where she will attend a traditional Ottoman shadow puppet show, a fashion show and visit a mosque to listen to Quranic recitals.