Sullivan spoke to reporters aboard Air Force One as President Joe Biden flew to India to attend a G20 summit.
“Many of the elements of a pathway to normalization are now on the table. We don’t have a framework, we don’t have the terms ready to be signed. There is still work to do,” Sullivan said.
He added there was a “broad understanding of many of the key elements,” without going into detail.
US officials see a potential deal between Israel and Saudi Arabia as possible after the administration of then-President Donald Trump reached similar agreements between Israel and Morocco, Sudan, Bahrain and the United Arab Emirates.
Biden said on CNN in early July that Israel and Saudi Arabia were a long way from a normalization agreement that would involve a US-Saudi defense treaty and a civilian nuclear program for the Saudis from the United States.
Biden envoy Brett McGurk was in Saudi Arabia for talks this week that officials said was largely about the Yemen war but was also expected to include discussions on the potential normalization deal.