The current American president (Donald Trump) is very sympathetic to the Kurds. They should make the maximum advantage out of this, and demand an autonomous state for the Kurds in South-east Turkey.
Erdogan would never agree to this and would more likely repeat the Armenian genocide on the Kurds than give them independence. However maybe if they can figure something out with Iraq and Syria and create an autonomous Kurdistan there Turkey will be more likely to agree to some compromise. As it is now they don't even acknowledge the existence of the Kurdish ethnic group.
Turkey is against the creation of an independent or autonomous Kurdistan in Northern Syria. Moreover, the Kurdish faction in Syria (YPG) is closely affiliated with the PKK (which is classified as a terrorist organization in Turkey).