The American intelligence officials reportedly told the Israelis not to share sensitive information with Mr Trump's aides until the incoming president's relationship with Russia had been fully investigated.
The claim was made in the Israeli newspaper Yedioth Ahronoth and cannot be confirmed.
A spokesman for Benjamin Netanyahu did not respond to a request for comment, and the CIA also declined to comment.
But if true it underscores the extraordinary state of relations between Mr Trump and US intelligence, with American spies openly warning foreign allies that the new president may be compromised by Russia.
The Yedioth Ahronoth story, written by the investigative journalist Ronen Bergman, claimed to have details about a recent meeting between American and Israeli intelligence officials.
"Israeli officials who attended that meeting said that their American counterparts spoke despairingly about the election of Trump, who has repeatedly lashed out at the American intelligence community," Mr Bergman wrote.
He continued: "The American officials went on to say that they believed that Putin has 'levers of pressure' over Trump—but refrained from going into any detail."
The potential leverage referred to is believed to be a dossier of unverified but potentially explosive allegations against Mr Trump which was compiled by Christopher Steele, a former MI6 agent.
Comment: It has been verified -- as being complete horse hockey.
- Pack of lies: Demolishing the 35-page report alleging Trump's 'Russian cultivation'
- The war for your mind: Fake 'Trump Dossier' could have been easily verified
- The Atlantic slams BuzzFeed for revealing how stupid CNN's 'Trump Dossier' story really was
- A Tale of Two Dossiers: Putin, Trump and the CIA
The dossier was known to US intelligence for months before it erupted into the public sphere this week.
Comment: Translation: It was shopped around for months and no one would touch it because it was so preposterous. Idiot McCain took the bait.
Mr Trump has strongly denied that Russia has any leverage over him. On Friday, he tweeted that the "phony allegations against me were put together by my political opponents and a failed spy afraid of being sued".
While relations between the US and Israeli governments have often been publicly tense during the Obama administration, their spy agencies have worked closely together.
The two sides collaborated on Operation Olympic Games, a covert campaign of cyber warfare designed to sabotage Iran's nuclear programme. Israel is alleged to have also assassinated four Iranian nuclear scientists as part of its effort to disrupt Iranian nuclear development.
While Israel has cordial relations with Russia, Israeli intelligence would be afraid that any secrets which reached Moscow might then be passed on to Tehran. Russia and Iran are both fighting on the side of the Assad regime in Syria and are known to share some intelligence.
"The Israelis who attended the meeting said that the Americans advised them not to expose any sensitive sources to members of the Trump administration, lest that information reach Iranian hands, until it becomes clear that Trump does not have a compromised relationship with Russia and is not vulnerable to extortion," the Yedioth Ahronoth story said.