Netanyahu's allies were set for fresh negotiations with representatives of Lieberman's far-right Yisrael Beitenu party to try to entice it to join the governing coalition and boost its currently wafer-thin majority in parliament.
Leaks to the Israeli media from both sides said a deal was close to being finalised.
Yisrael Beitenu holds six of the 120 seats in parliament and its entry into government would be a major boost for Netanyahu, who has not concealed his ambition to expand on the coalition's current 61 seats.
As defence minister, Lieberman, who himself lives in a Jewish settlement in the occupied West Bank, would oversee military operations in the Palestinian territories and have a major say in policy towards the settlements.
The international community considers the settlements illegal and regards their persistent expansion by successive Netanyahu governments as one of the biggest obstacles to peace.
Since its formation in May 2015, Lieberman had repeatedly branded the current five-party coalition as "defeatist" but yesterday he told a news conference that he would be open to joining it if key demands were met.
Lieberman has long expressed mistrust in Palestinian president Mahmud Abbas and called for his removal.
Just a month ago, he said that if he were defence minister, he would give Hamas's Gaza leader Ismail Haniya 48 hours to hand over detained Israeli civilians and the bodies of soldiers killed in the 2014 war "or you're dead".
The Palestinians said they would wait for confirmation of Lieberman's appointment before making a formal response, but one official said it would be a "disaster" for Palestinians living under Israeli occupation.
He said such was the dislike of Lieberman that he was a "unifying factor for Palestinians.
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