"I want to ask the Palestinian Authority and chairman Arafat: 'If you want, I would like to be a Palestinian citizen'," Vanunu told Israeli private television late on Tuesday.
The Israeli, who has taken refuge in St George's Anglican cathedral in occupied east Jerusalem since his release in April, has frequently said he wants to leave Israel where he is widely reviled for not only for exposing Israel's nuclear arsenal and clandestine weapons programme, but also for converting to Christianity.
Shrugging off the Israeli public's negative image of him, he said: "Six billion people respect what I did, so if six million Jews don't respect it, it doesn't matter. I don't feel like a traitor."
Since his release on 21 April after 18 years in prison, Vanunu has been subject to broad restrictions, including a ban on travelling abroad as well as holding unauthorised meetings with foreigners.
"I want to have a wife ... and to build a family and live like a normal human being," he told Israel's Channel 2, speaking in English.
Vanunu was abducted by Israeli secret service agents in Italy, smuggled back to Israel and then jailed in 1986 after leaking top-secret details about the Dimona plant to Britain's Sunday Times.