The Portuguese attacker, who is at the World Cup with his country at present, now has two offers from the Arab nation.
Ronaldo was previously linked by the media to Al Nassr, rivals of Al Hilal.
Marca in Spain reported the initial links, while The Express in England are now adding information about the bid from Al Nassr.
The two clubs are the most successful in Saudi Arabia's domestic league, with Al Hilal having 18 league titles to Al Nassr's nine.
Ronaldo may not be able to continue his career in Europe, if reports are to be believed, as interest in him from clubs on the continent is limited.