Speaking at a conference in Washington on Friday night, video of which was released by his office, Lieberman was quizzed about the vote which could go to its first reading next week.
"I think it's much better to postpone all this legislation and steps until January 20," he said, speaking in English.
US President Barack Obama officially hands over office to Trump on that date.
"My proposal is to wait for the new administration and to create, together with the new administration, a common policy without any uprise and not to create facts but to wait and to discuss with the next administration our policy and our visions.
"I think it makes sense," Lieberman said.
Israeli right-wingers hailed Trump's November 8 election triumph which they hope will usher in a US administration far less critical of settlement expansion than under Obama.
A scheduled first reading Wednesday of a bill to legalise around 4,000 settler homes in the occupied West Bank was postponed until December 5.
Israeli media reported that the delay was because efforts were still being made to secure a majority.
The settlement bill has tested Prime Minister Benjamin Netanyahu's coalition, widely seen as the most right-wing in the country's history.
Netanyahu does not want the bill to pass, warning that it could violate international law and result in repercussions at the International Criminal Court.
Countries including the United States have also strongly criticised the bill and Netanyahu is concerned over an international backlash.
But he is also faced with holding together his coalition and not being seen as acting against the powerful settler movement.
Israel's attorney general says the legislation will never hold up in court.
But those who support it say the move is urgently needed to protect a Jewish outpost in the occupied West Bank called Amona.
The outpost, where around 40 families live, is under a high court order to be demolished by December 25 because it was built on private Palestinian land.
The bill, however, goes far beyond legalising Amona and would allow an estimated 4,000 Jewish homes in the West Bank to be legalised, according to settlement watchdog Peace Now.
Agence France-Presse
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