Israel's regional cooperation minister said on Thursday that he had asked Saudi Arabia to admit direct flights from Tel Aviv for Muslim pilgrims, pointing to a possible new accommodation by Riyadh ahead of next week's visit by US President Joe Biden.
Israeli officials have also been seeking expanded permission for their airlines to fly over Saudi soil to Asian destinations.
Saudi Arabia, Islam's birthplace, does not recognise Israel and has said nothing of possible bilateral developments during Biden's visit. Israel has also shied from drawing such links.
But Israel's Regional Cooperation Minister Esawi Freij said Israel has been working to bring what he deemed "under the counter" contacts between the countries - based mostly on commercial interests and shared worries about Iran - more into the open.
"I want to see the day when I can depart from Ben-Gurion (airport near Tel Aviv) to Jeddah to fulfil my religious obligation" of pilgrimage to Mecca, said Freij, a member of Israel's 18% Muslim minority.
"I took this matter up with Saudi Arabia and I really hope that day will come," he told Israel's Army Radio, without expanding on where or when such discussions took place.
Saudi Arabia has long admitted Muslim pilgrims from Israel, but they must travel through third countries. That ends up costing around $11,500 for a week-long stay, Freij said. Pilgrims from neighbouring Arab countries pay around half that.
When the United Arab Emirates and Bahrain established relations with Israel in 2020, Riyadh signalled its assent by providing a Saudi air corridor for Israeli planes headed to those Gulf states.
"We are in talks on getting general (Saudi) over-flight rights for destinations other than Dubai, Abu Dhabi or Manama. This will save significant times for reaching Asian destinations, for example," an Israeli official told Reuters.