“There’s a rapprochement maybe under way,” Biden told contributors to his 2024 re-election campaign at an event in Freeport, Maine.
The president did not give details about the possible deal.
US officials have sought for months to reach what would be a historic agreement between the long-time adversaries but the Saudis have been resistant.
New York Times columnist Thomas Friedman, in a piece published on Thursday, said Biden was considering whether to pursue a US-Saudi mutual security pact that would involve Saudi Arabia normalizing relations with Israel.
White House national security adviser Jake Sullivan was in Jeddah this week with Middle East envoy Brett McGurk discussing the possibility of a normalization deal, White House officials confirmed.
US officials see a potential deal between Israel and Saudi Arabia as possible after the administration of former President Donald Trump reached similar agreements between Israel and Morocco, Sudan, Bahrain and the United Arab Emirates.
The potential deal, if reached, would be a turnaround for a US administration that has been losing its influence in the region and whose ties with Saudi Arabia have been strained since Biden took office.