The official, with the Justice Ministry, said Samar Halami Abed Allatif al-Barak's request was submitted to the court Sunday, The Jerusalem Post reported.
The court was expected to decide Monday whether to extend al-Barak's detention.
The Shin Bet (security agency) was expected to ask that al-Barak be held for another six months, Haaretz said.
Israeli army officials warned the release of al-Barak, considered an expert in unconventional weapons, would aid the jihadist infrastructure in the region, Israel Radio reported.
Al-Barak was born in the West Bank city of Qalqilya in 1974 and studied microbiology in Pakistan, Haaretz said. He had military training in Afghanistan in 1998 and three years later was recruited by al-Qaida, the newspaper said.
Al-Barak had been arrested by American authorities and imprisoned in Jordan because of alleged terrorist activities, Haaretz said.
When al-Barak's administrative detention was last extended in July, an Israeli military prosecutor warned he has connections to al-Qaida leadership and said his release would pose a threat to Israel, the newspaper reported.