Saudi Arabia does not recognise Israel and lifting the 70-year-old airspace ban would reflect what appears to be thawing ties between Israel and the kingdom.
Israeli Prime Minister Benjamin Netanyahu said on Monday that Saudi Arabia had granted Air India permission to fly over its territory on its new routes to and from Tel Aviv.
There was no immediate confirmation from either Saudi officials or Air India.
Netanyahu made the announcement during a briefing in Washington to Israeli reporters after he had met US President Donald Trump.
Saudi Arabia does not recognise Israel and lifting the 70-year-old airspace ban would reflect what appears to be thawing ties between Israel and the kingdom, both US allies with a shared concern over Iranian influence in the region.
Last month, Air India announced the planned thrice-weekly flights to Tel Aviv over Saudi soil, but the General Authority of Civil Aviation in Riyadh said at the time it had not granted such permission to the carrier.
El Al Israel Airlines, the country's flag carrier, flies four weekly flights to Mumbai.
These take seven hours as they fly south toward Ethiopia and then east to India, avoiding Saudi airspace. Israeli media says that Saudi overflight routes could reduce travel time by more than two hours.