“I think there is a window of opportunity right now,” Mr Herzog said. “This [US] administration would like to do it, our government would like to do it, I understand there is Saudi openness to doing it.”
The Biden administration has said that helping Saudi Arabia and Israel to establish diplomatic relations was a “priority.”
Administration officials have made several trips to the region in recent months, meeting Israeli, Saudi and Palestinian leaders to discuss what a deal might look like.
Mr Herzog was speaking at an event hosted by the Atlantic Council in the US capital for the third anniversary of the Abraham Accords, which saw the UAE and Bahrain establish relations with Israel.
He said the Biden administration's efforts to bring about a deal between Israel and Saudi Arabia was providing an opportunity for hope.
“I’m more hopeful now than I was a few months ago,” Mr Herzog said.
A Saudi-Israel deal would be a signature foreign policy win for US President Joe Biden, who is seeking re-election in 2024.
“It's a real opportunity regarding the potential for normalisation between Israel and Saudi Arabia,” said Daniel Shapiro, senior advisor for regional integration at the US State Department.
Mr Shapiro, a former US ambassador to Israel under president Barack Obama, was recently given the task of helping to steer the Negev Forum.
Established in 2022, the forum provides a framework for regional co-operation between the UAE, Israel, Bahrain, Morocco, Egypt and the US.
Saudi Arabia has long maintained that it will not pursue normalisation with Israel until progress towards peace with the Palestinians is achieved.
Mr Shapiro said that there was “potentially a Palestinian component” to a future deal.
Mr Herzog agreed: “I hope that they will draw the conclusion and rather than try to block it this time, they will join.”