The five apartment buildings, home to about 30 families, would be moved several hundred yards to land that is not privately owned by Palestinians, under the plan Netanyahu presented to his Cabinet on Sunday.
The plan to relocate the actual buildings, instead of razing them and rebuilding new ones, also would save the government money.
The plan requires the approval of Israeli Attorney General Yehuda Weinstein.
Israel's Supreme Court ruled in September that the neighborhood should be razed, siding with a lawsuit filed by Palestinians who said they owned the land.
As part of the plan, Netanyahu said that 10 housing units would be built in the settlement for every one moved. The change requires the attorney general's approval.
Another part of the plan would require the state to fight aggressively any future legal petitions on the issue.
Netanyahu reportedly presented the plan in an effort to avoid legislation on the issue, which he said would not help the settlements and other West Bank neighborhoods facing similar evacuation or destruction.
"Our policy is to bolster the settlements while adhering to the law," Netanyahu said. "We could always go for a legislative solution, but that has its prices, including in the international arena."
The Knesset is set to vote Wednesday on a bill that would override a Supreme Court decision to remove the buildings. The legislation would retroactively legalize buildings built on contested land if the owner does not challenge the construction within four years.
Netanyahu has prohibited his government ministers from voting for the legislation.