Israel gave the United States a document last week with its conditions for a diplomatic solution to end the war in Lebanon, Axios reported, citing two US officials and two Israeli officials.
Israel has demanded its forces be allowed to engage in "active enforcement" to make sure Hezbollah doesn't rearm and rebuild its military infrastructure close to the border, Axios reported, citing an Israeli official.
Israel also demanded its air force have freedom of operation in Lebanese air space, the report added.
A US official told Axios it was highly unlikely that Lebanon and the international community would agree to Israel's conditions.
The White House could not be immediately reached outside regular business hours. The US State Department did not immediately respond to a request for comment.
The embassies of Israel and Lebanon in Washington did not immediately respond to a request for comment.
White House special envoy Amos Hochstein is visiting Beirut on Monday to discuss a diplomatic solution to the conflict, the report added.

Trump says there will either be a deal with Iran or US will 'finish the job'
Storms kill at least eight in central China as Typhoon Bavi looms offshore
Landslide in China's Gansu province traps 16
Hamas dissolves Gaza government, Israel dismisses move as 'stunt'
Death toll from Venezuela quakes rises to 3,535 as thousands remain displaced