Musannaf Ibn Abi Shayba 16:232

Abu Bakr narrated to us, he said: Hafs narrated to us, from Hisham, from his father, who said: Umar ibn al-Khattab came out from the privy (toilet), and food was brought to him. They said, "Shall we call for water for ablution (wudu)?" He said, "I only eat with my right hand and I cleanse myself with my left hand." So he ate and did not touch water.