All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
What you have mentioned in the question is not a Hadeeth of the Prophet and it does not exist in the books of Sunnah and its registers.
The author of As-Seerah Al-Halabiyyah mentioned it without stating any chain of narrators, saying: "Some said that Al-Muqawqis sent a doctor with the gift to the Prophet who said: 'Go back to your people. We are a people who do not eat until we are hungry. And when we eat, we do not eat to our fill.'" [End of quote]
Al-Albaani said about it in his book As-Silsilah As-Saheehah (7/1651 -1652): "There is no basis for it."
Allah knows best.