There was no immediate comment from the Ligue 1 champions, owned by Qatar Sports Investments, but French newspaper L'Equipe said the deal could net Neymar €160 million.
The transfer fee was reported to be about €90 million plus add-ons, and the move is subject to the player completing a medical.
Sources close to the operation told Reuters that Neymar was having a medical in Paris on Monday and was expected to arrive in Riyadh on Wednesday to be presented to fans at King Fahd Stadium.
Al Hilal, managed by Portuguese coach Jorge Jesus, play Al Feiha on Saturday with Neymar expected to wear the number 10 shirt.
The Brazilian was contracted to stay in the French capital until 2025 and has 118 goals in 173 appearances, capturing numerous trophies including five Ligue 1 titles, but is no longer considered a key player in coach Luis Enrique's squad.
Multiple sources said he had hoped to return to Barcelona on a loan agreement but the Spanish side's financial issues had made that unaffordable.
Al Hilal had tried to sign PSG's France international Kylian Mbappe, who was reinstated into the Paris club's first team on Sunday. The Saudi side were also reportedly interested in Argentinian Lionel Messi who opted to join Major League Soccer's Inter Miami.
The most successful club in Saudi Arabia and Asia, Al Hilal have won 66 trophies and hold the record for league and Asian Champions League titles, with 18 and four of them respectively.
Strengthening the squad is a priority for the Riyadh-based club, as the Saudi Public Investment Fund announced in June an investment and privatisation project for sports clubs involving league champions Al Ittihad, Al Ahli, Al Nassr and Al Hilal.
The Saudi Pro League season kicked off on Friday after spending close to half a billion dollars luring a host of top players and coaches from European powerhouses.
Cristiano Ronaldo joined Al Nassr last season soon after the World Cup in a deal which made him the highest-paid athlete on the planet, while Al Ittihad signed Karim Benzema from Real Madrid.
Champions League winners Riyad Mahrez, Edouard Mendy and Roberto Firmino have all signed for Al Ahli.
