Zaha is nearing the end of his contract at Selhurst Park and is set to leave the club for free at the end of this week.
The 30-year-old does not lack suitors though, with clubs offering lucrative salaries to secure his services.
While Al-Nassr’s offer is by far the best, according to Turkish journalist Elis Buse Arac, other clubs are also trying.
Turkish side Fenerbahce, who are also keen, have proposed the best offer in Europe, worth around €4.5m along with a signing-on fee.
Premier League side Crystal Palace, for whom Zaha currently plies his trade, are offering a contract extension worth €4.2m.
The ball is now in Zaha’s court as he makes a final decision on his future.
Zaha’s association with Crystal Palace runs back to 2004 when he joined them as a youngster.
He joined Manchester United in 2013 only to leave them for the Eagles two years later.