The Prophet ﷺ used to sleep until he could be heard breathing deeply, then he would get up and pray without performing ablution.
حدثنا وكيع حدثنا الأعمش عن إبراهيم عن الأسود
كان النبي ﷺ ينام حتى ينفخ ثم يقوم فيصلي ولا يتوضأ
Its chain of transmission is sahih. It is found in Ibn Majah 1/160 no. 475, and Ibn Abu Shayba 1/132, both in the chapter on purification.