According to the Turkish source, Al-Nassr are willing to pay Ozil, 31, a stunning $20m (€16.8m) tax-free per year.
Officials from the club contacted Ozil’s camp to try and strike an agreement for the Germany midfielder.
If they are unable to land him now, they hope to strike a preliminary deal to sign Ozil next year.
Al-Nassr chiefs reportedly told Ozil, “We want to make you the new Prince of Saudi Arabia and we will not spare any sacrifices for this.”
Ozil has previously said that he will see out the remaining year of his Arsenal contract.
However, the former Real Madrid star is out of favour at the Emirates and is said to be considering the Saudi offer.
Ozil also has interest from Fenerbahce, China, Qatar and the USA.