Salah, Liverpool's record Premier League scorer, was strongly linked with a move to Al Ittihad by Saudi and English media in the close season last year as the Saudi Pro League set about recruiting some of the sport's biggest names.
Former Real Madrid captain and Ballon d'Or winner Karim Benzema and his French compatriot N'Golo Kante moved to Al-Ittihad, while Al-Hilal signed Brazilian Neymar from Paris St Germain, after Al-Nassr had pulled off a stunning deal to sign Cristiano Ronaldo in January 2023.
The Saudi Sports Recruitment Program, which is overseen by the sports minister, is responsible for player contracts.
"We received a statement from the club that there is a desire to sign Mohamed Salah. The amount was astronomical of course," Prince Abdulaziz bin Turki Al Faisal, told the Thmanyah podcast.
The sports minister explained that the amount on offer was astronomical even compared to the deals with Neymar, Ronaldo and Benzema.
"The deal was for a one-year loan. Salah's contract was valid (with Liverpool), and therefore we cannot negotiate with him without returning to the club," he added.
"We inquired through the (Sports Recruitment) program with the club itself whether there is a desire to dispense with Mohamed Salah and they told us no... and this closed the matter decisively because the club does not want to let him go."
The 32-year-old Egypt international, who scored 25 goals in 44 games in all competitions for Liverpool last season, has a contract with the Premier League club until 2025.