It is understood that Israel's strategic affairs minister Ron Dermer has told Mr Trump and his adviser son-in-law Jared Kushner that the country is rushing to establish arrangements to halt its war with Hezbollah.
The peace plan would be a special present to the future President, who has vowed to halt conflicts in the Middle East and the war caused by Russia's invasion of Ukraine.
But it is believed that any end to fighting between Israel and Hamas in the Palestinian enclave of Gaza may take longer.
Israel carried out further air strikes on Beirut yesterday, with raids on the Lebanese capital's southern suburb of Dahieh.
There were also strikes at Salahaddin School, where displaced Palestinians were sheltering, in the Rimal district of Gaza.
A deal to halt Israel's attacks in Lebanon would be seen as a coup for Mr Trump.
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