The bill has drawn harsh criticism internationally, with its main backer, Education Minister Naftali Bennett, calling it the start of Israel's eventual annexation of most of the West Bank.
It would still need preliminary approval and three full votes at Israel's Knesset, or parliament, but an agreement between Netanyahu and Bennett would likely assure passage.
The bill has severely tested Netanyahu's coalition, seen as the most right-wing in Israeli history. A previous version was given preliminary approval last month.
Netanyahu told a meeting of members of his Likud party that "we have worked very hard to find a solution", while Israeli media reported that a compromise was at hand.
The international community considers all settlements in Israeli-annexed east Jerusalem and the West Bank to be illegal, whether they are authorised by the government or not.
The Israeli government differentiates between those it has approved and those it has not.
Amona, where around 40 families live, is under a court order to be evacuated by December 25 since it was built on Palestinian land.
Some members of Netanyahu's coalition had previously said they could not support the bill if Amona remained part of it because of the court ruling against it.
The agreement will instead see Amona residents temporarily moved to nearby land that Israeli officials describe as abandoned, until a permanent solution is found.
Rights groups, however, say that land too is owned by Palestinians and that the move would violate international law.
The UN envoy for the Middle East peace process, Nickolay Mladenov, said the legislation "has the objective of protecting illegal settlements built on private Palestinian property in the West Bank.
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