The Belgian has been at the heart of City's unprecedented dominance since joining from Wolfsburg in 2015.
The 33-year-old's contract with the Premier League champions expires at the end of the season and there has been no clear indication on his future in England.
Ronaldo is a huge admirer of De Bruyne and has made a personal plea to the Al-Nassr's hierarchy to try and tempt him to join the club, according to The Sun.
The Portuguese star wants his side to go all out for De Bruyne and believes it would be a huge coup for the Saudi Pro League.
Cristiano Ronaldo has urged Al-Nassr to make Kevin De Bruyne an offer he can't refuse
Mail Sport revealed back in February that Saudi Pro League officials are ready to intensify their efforts to lure De Bruyne away from the Premier League.
When asked about the potential of a switch to the Middle East, De Bruyne - who already earns £300k-a-week at City - admitted this summer that the 'incredible amounts of money' on offer make it an attractive destination that would be hard to turn down.
'I still have one year left on my contract, so I have to think about what could happen,' he told Belgian newspaper Het Laatste Nieuws.
'My eldest is now eight years old and knows nothing but England. He also asks how long I will play for City. Once the moment comes, we will have to deal with it in a certain way.
'At my age you have to be open to everything. You're talking about incredible amounts of money in what may be the end of my career. Sometimes you have to think about that.'
De Bruyne added: 'If I play there for two years, I will be able to earn an incredible amount of money. Before that I had to play football for 15 years. I may not even reach that amount yet.
'Then you have to think about what that could mean next. But at the moment I haven't had to think about that yet.'
De Bruyne is currently sidelined with a hamstring injury and has missed City's last six matches.
He has scored 103 goals and provided 171 assists in 388 appearances since his move to the Etihad nine years ago.
In that time, he has won six Premier League titles, two FA Cups, five League Cups as well as the Champions League.