Saudi Arabia signalled approval for Israel's US-sponsored forging of ties with Gulf neighbours United Arab Emirates and Bahrain in 2020 but has held off on following suit, saying Palestinian goals for statehood should be addressed first.
Any such prospects have been further clouded, however, by Riyadh's strains with US President Joe Biden, its recent fence-mending with regional rival Iran - a foe of Israel - and the rise of Benjamin Netanyahu's hard-right Israeli government.
Netanyahu's centrist predecessor, Yair Lapid, said on March 10 that, as prime minister last year, he secured Saudi consent for what would be the first direct Haj flights from Israel, some 18% of whose population is Muslim.
Riyadh has not offered confirmation.
Asked whether the direct flights would happen for next month's pilgrimage to the holy Saudi city of Mecca, Israeli Foreign Minister Eli Cohen said a request had been submitted.
"This issue is under discussion. I cannot tell you if there is any progress," he said in an interview with Israel's Army Radio. "But with that, I am optimistic that we can advance peace with Saudi Arabia."
The Biden administration last June predicted there would be direct charter flights from Israel to Saudi Arabia for the Haj. But a senior US official briefed on the matter told Reuters on Wednesday that it was unclear if the flights would go ahead.
Muslims from Israel and the Palestinian territories currently travel to Mecca through third-party countries, which can spell additional expense and bother.
Saudi Arabia has been allowing Israeli airlines to overfly it to UAE and Bahrain since 2020, a corridor that it and next-door Oman have since expanded to include other destinations.
