Benzema, 35, had signed a one-year contract extension to stay in Spain last season but has yet to receive any notice from his current club on his status for the next season.
The reports said that the Frenchman had initially turned down an offer from Al-Ittihad but was now contemplating moving to Saudi Arabia after the club upped his value.
Benzema joined Real Madrid in 2009 from Olympique Lyon and has since scored 353 goals and provided 165 assists in 647 matches.
In the 2022 to 2023 season, he grabbed 30 goals and six assists in 42 matches across competitions despite suffering an injury.
If he accepts the offer, the striker would follow in Ronaldo’s footsteps as the second big football name to move to the Kingdom.
Ronaldo moved to Al-Nassr in January from Manchester United with a contract worth over $200 million per year.
Several media reports have also claimed that another Saudi club was also vying for Argentinian football icon Lionel Messi but his father denied the claims.