"I have been singled out as a target. My life is in danger," Sultan was quoted as telling the Israeli daily Yediot Achronot.
Sultan, who has served as ambassador to Cairo for the past three years, said he had asked to be moved to a different assignment six months ago.
But he said that when nobody was found to take his place in Cairo — which he described as a "difficult posting" — he consented to stay on in the Egyptian capital.
Foreign Ministry officials said discussions had been under way for at least a year about changing Sultan's post.
Yediot Achronot mentioned one possible replacement — Haifa University Professor Yosef Ginat, an anthropologist who headed the Israeli academic center in Cairo for four years and who is said to have good ties with the Egyptian government and in intellectual circles.