The 40 families living at Amona, in the northern part of the Israeli-occupied West Bank, face a court order to leave the site by December 25 because it was found to have been built on private Palestinian land.
Netanyahu is seeking a way out of an impasse which has put him between Israel's Supreme Court and the legal opinion of his own attorney general on one hand, and the anger of settlers who are a key part of his political constituency on the other.
"Until dawn this morning we made very great efforts to reach an agreed solution on Amona," Netanyahu told ministers and media at the weekly cabinet meeting, referring to a last-ditch overnight meeting with settlers and ministerial colleagues.
"We did the maximum. Now I can only hope that the Amona residents, who are at this moment discussing the proposal among themselves, will accept it."
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Media said the latest draft proposed moving 24 of the 40 families to plots adjacent to the current site which are not covered by the Supreme Court ruling.
Supporters of the Amona families, many of them youngsters, have been arriving at the outpost for days in a show of solidarity that some fear may turn violent if they are forcibly evicted.
An AFP journalist at the site said they were building barricades, drilling into floors and welding obstacles.
"I came to make a statement. We are not giving up," said a 19-year-old man who refused to give his name.
The residents have been debating the offer since Sunday morning and some media reports predicted it might be hours more before they announce a decision.
Tweets from a settlement spokesman gave no details of the offer or the mood at the meeting but the head of the Amona "struggle committee" said it was an improvement on a proposal the residents turned down on Thursday.
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