The government confirmed it was considering the authorisation in a court document first made public by rights group Yesh Din, which has been involved in legal action against one of the outposts.
The international community regards all Jewish settlements in the West Bank as illegal, but the Israeli government makes a distinction between those it has authorised and those it has not.
The wildcat outposts, often little more than a few caravans, are notorious for housing young Jewish hardliners, referred to in Israel as hilltop youth.
Settlements and outposts are seen as major stumbling blocks to peace efforts as they are built on land that Palestinians see as part of a future state.
Israeli Prime Minister Benjamin Netanyahu, who addresses the UN General Assembly on Thursday, has faced major criticism internationally for refusing to halt settlement expansion. The government did not respond to requests for comment from AFP.
Yesh Din has been involved in legal action in a bid to force Israel's government to remove the Adei Ad outpost, established in 1998.
In a court document filed in the case, the government said it opposed removing the outpost because it was considering authorising it along with others in the area.
Signup to our newsletter and follow us on Facebook and Twitter!
Haaretz newspaper said the review involved a total of five outposts covering six square kilometres (2.4 square miles).
"The state is willing to do so though it admits the outpost was established in violation of the law, and many structures in it were built illegally," Yesh Din said in a statement, referring to Adei Ad.
Yesh Din has argued that Adei Ad should be removed "not only because it is constructed illegally, in part on land owned privately by Palestinians, but also because it serves as a hub for criminal activities and grave violence, leading to systematic human rights violations of the Palestinian residents in its vicinity."
Residents of Adei Ad deny involvement in so-called price-tag violence, the term for nationalist hate-crimes committed against Palestinians, Christians and even the Israeli military by Jewish extremists.
Israel occupied the West Bank in the 1967 Six-Day War in a move never recognised by the international community.
Hardline Jewish nationalists see the entire West Bank as part of Israel, which refers to the territory as Judea and Samaria, the names for the ancient biblical kingdoms located there.
On July 31, suspected Jewish extremists firebombed a Palestinian home in the village of Duma that killed toddler Ali Saad Dawabsha and his parents.
Duma is near the outposts the government is considering authorising.