Since the start of the war, the Houthis have launched multiple attacks on Eilat and the Red Sea area.
According to the report, the US request is driven by concern that Israeli retaliation might spark a wider regional conflict.
The report, which cited US and other government officials, said that the US requested that Israel allow the American military to deal with the Houthis instead.
On Wednesday, Reuters reported that Saudi Arabia has asked the United States to show restraint in responding to attacks by Yemen's Houthis against ships in the Red Sea.
According to the report, the sources said that Riyadh's message of restraint to the US was aimed to avoid further escalation. Riyadh was so far pleased with the way the United States was handling the situation, the sources added.
The White House declined to comment on the report, and the Saudi government did not respond to an emailed request for a comment on the discussions.
