There was no immediate confirmation from either Saudi officials or Air India. Mr 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.
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 have said that Saudi overflight routes could reduce travel time by more than two hours.