One source said the club were in “serious negotiations” with the 37-year-old but an agreement had not yet been reached because of issues with Ronaldo’s image rights.
The Portuguese forward left United last month after giving an explosive television interview in which he took aim at the club and coach Erik ten Hag.
Ronaldo will sign a two-and-a-half year deal worth nearly 200 million euros ($210 million) a season, starting in January, according to a report by Spanish newspaper Marca.
However, another source at the Saudi club told AFP that nothing had been signed.
Ronaldo said he had rejected a huge deal to join a Saudi club in his hard-hitting interview.
The five-time Ballon d’Or winner could join Colombian goalkeeper David Ospina and Cameroon midfielder Vincent Aboubakar, who currently play at Al-Nassr.
The Portugal captain became the first player to score at five men’s World Cups when he netted a penalty in their opening 3-2 win over Ghana in Qatar.
Portugal, aiming to win a first World Cup trophy, face Switzerland on Tuesday in the last 16.
The striker helped his team triumph at Euro 2016 and has won an impressive haul of silverware across a glittering club career with United, Real Madrid and Juventus.