Kylian Mbappe: Saudi Arabia's Al Hilal 'submit world-record bid' for French star
Fabrizio Romano, a reliable Italian journalist, said the deal is understood to be worth a record €300m ($333m) fee.
Mbappe's club, Paris Saint-Germain (PSG), "obviously accept" the bid, according to Romano. However, no talks with the player's entourage have taken place yet.
Al Hilal would offer the French star a "world-record salary - even if just for one season", the reporter added.
Mbappe, 24, was reportedly put on sale by PSG last week.
The player refused to extend his contract last month, raising speculation about his future with the Qatari-owned club.
PSG reportedly believe Mbappe has already agreed to move to Spain's Real Madrid next year when his contract is set to expire.
Al Hilal's bid comes as the Parisian club looks to offload the player for profit this summer, rather than lose him on a free transfer in 2024.
Since last year, teams playing in the Saudi Pro League have been targeting high-profile players in Europe, offering big fees and salaries.
The Saudi league's four biggest clubs - Al-Ittihad and Al-Ahli of Jeddah and Riyadh's Al-Hilal and Al-Nassr - were recently taken over by Saudi Arabia's Private Investment Fund (PIF), marking the first steps towards privatisation.
Al-Nassr signed Cristiano Ronaldo, one of the best players in the game's history, in December for a $200m-a-year deal that made him the highest-paid footballer of all time.
Since the start of this year's summer transfer window, Al-Nassr has signed Seko Fofana from Lens, Marcelo Brozovic from Inter Milan and Alex Telles from Manchester United.
Their local rivals Al Hilal have signed Ruben Neves from Wolverhampton, Sergej Milinkovic-Savic from Lazio, and Kalidou Koulibaly from Chelsea, paying a total of €118m ($130.9m) on the trio.
Jeddah club Al Ittihad signed the current holder of the Ballon d'Or, Karim Benzema, and his French teammate N'Golo Kante.
Their local rival Al Ahli have so far signed Edouard Mendy from Chelsea and Roberto Firmino, with more footballers being linked to the league.