The teenager turns 16 in June and transfer journalist Fabrizio Romano confirmed on Tuesday that the Saudi club is closely monitoring his development and considering first-team inclusion as one of the options for his next phase.
Ronaldo Jr followed his father to Saudi Arabia in 2023 and has been progressing through Al-Nassr's academy since.
He has attracted attention this season with a standout campaign at youth level, including a hat-trick for the Under-16 side.
He also recently trained with Real Madrid's Under-16 setup amid speculation about a potential future move to Spain.
His father, Cristiano Ronaldo, has spoken publicly about his desire to play alongside his son before his career ends.
"I would like it. It's not something that keeps me up at night, but I would like it. The years are starting to pass and obviously Cris will have to, one day, leave football. But it won't be a problem either, in my opinion," the 41-year-old has said.
No final decision has been taken, with the club expected to complete a review of Ronaldo Jr's physical and technical readiness at the end of the season.
A handful of other father-son combinations have played together professionally, including Rivaldo with Rivaldinho, Henrik Larsson with his son Jordan, and the Eastham family in the 1950s.
Ronaldo Jr has chosen to represent Portugal at youth level and made his debut in their Under-17 setup last year.