Israel's Channel two television on Saturday reported that Vanunu, who completes an 18 year prison term on 21 April, had sent a letter from the jail to the Israeli Interior Ministry asking to give up his citizenship.
Vanunu, it is understood, is seeking to give up his citizenship to avoid confinement in the country after his release.
But informed sources said Vanunu could find it difficult for his request to be granted. Interior Ministry regulations state only Israelis living abroad can renounce their citizenship.
Vanunu, who worked at Israel's main reactor in the southern town of Dimona, gave Britain's Sunday Times newspaper in 1986 details about the facility, leading independent experts to conclude Israel has more than 100 nuclear warheads.
Refusing to comment on Vanunu's request, an Interior Ministry spokeswoman has said all Israelis have the right to submit such a request, although not all cases are approved.
"It depends on many factors and individual circumstances," she said. "Every case is different. Every Israeli has the right to submit a request to give up his or her citizenship, but there is no guarantee it will be approved."
Israeli security sources have said Israel will ban the former atomic reactor technician from travelling abroad after his release for a probationary period, and monitor him closely.