Pompeo, who served as Trump's CIA director and top diplomat, made the comments in a recorded video address to the Combat Anti-Semitism Movement, which will give him its inaugural Global Leadership Award on Monday.
Under the Abraham Accords brokered by Trump last year, four majority Arab states - the United Arab Emirates, Bahrain, Morocco and Sudan - agreed to establish ties with Israel.
The Israeli press was rife with speculation about other Arab nations interested in joining the pact, with powerhouse Saudi Arabia widely regarded as a top prize for the Jewish state.
"Predicting the future has proven a struggle for me," Pompeo said in remarks shared with AFP, adding that he thinks "many more" countries will seek ties with Israel.
"I hope that the Kingdom of Saudi Arabia can find its way to join the Abraham Accords. I know that many inside that country want that to take place," he said.
Sources in Jerusalem have said Pompeo and Israeli Prime Minister Benjamin Netanyahu met with Saudi Crown Prince Mohammed bin Salman in November in the Red Sea city of Neom.
The meeting, denied by Riyadh, fuelled frenzied speculation in Israel that a normalisation deal might be close.
Publicly the kingdom has affirmed its decades-old policy of not establishing ties with Israel until a deal is reached to resolve the Palestinian conflict.
The Trump administration courted Riyadh as it sought to isolate common foe Iran and withheld tough criticism of alleged right abuses in the kingdom, including over the gruesome 2018 murder of Saudi journalist and royal critic Jamal Khashoggi.
Breaking with Trump's approach, President Joe Biden said Friday Washington would "hold (Saudi Arabia) accountable for human rights abuses" as it released an intelligence report accusing Prince Mohammed of approving Khashoggi's murder by Saudi agents in Istanbul.
Soleimani
Pompeo further claimed the Abraham Accords were made possible by the US killing of powerful Iranian general Qasem Soleimani in an air strike, arguing it built trust between Washington and its Arab allies.
"When leaders in the Arab world saw that the United States was prepared to do this, to push back against Iran, to push back against the IRGC (Islamic Revolutionary Guard Corps) leadership in the person of Qasem Soleimani, they knew they had a friend," Pompeo said.
"They knew that they could... build out a set of accords with the State of Israel: these are not disconnected issues, they are deeply connected, one could not happen without the other."
A United Nations special rapporteur on extra judicial killings, Agnes Callamard, said Soleimani's killing was "unlawful".
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