The superstar's £170million per season Al-Nassr contract expires in 2025.
And it seemed to present an opportune moment to move to rival Al-Hilal in time for the June Club World Cup.
It's move which could see Inter Miami's Lionel Messi share the pitch with Ronaldo as they did for many iconic years in Spain for Barcelona and Real Madrid.
The forward would also face his former side if he were to jump to the other side of Riyadh as Al-Hilal were drawn into Group H with Real Madrid, RB Salzburg and Pachuca.
However, in an interview with GiveMeSport Calzada said: "That sounds like science fiction.
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"Cristiano Ronaldo is not our player so it's difficult to comment on that. He's not a free agent just now, so it's not nice to talk about that."
January 2023 was the last time we saw Ronaldo and Messi go head-to-head.
Paris Saint-German faced off against the Riyadh All Stars, a Saudi Pro League representative team, which was Ronaldo's debut in Saudi Arabia.
The French team won 5-4 with Messi netting the first and Ronaldo scoring a brace.
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If Ronaldo were to join Al-Hilal he would play alongside Neymar, Joao Cancelo and Premier League cult hero Aleksandr Mitrovic.
Calzada was also questioned about rumours Mohamed Salah could join the side when his Liverpool contract expires next summer.
But the CEO gave little away as he said: "We are not commenting on rumours. We have a policy of not commenting on rumours."
Reportedly Ronaldo has begun contract negotiations with his current club as he is settled in Saudi Arabia and aims to hit 1,000 career goals.
For club he has netted 775 times while his tally for Portugal is 135, so he currently sits just 90 goals away from the four figure number.
The 39-year-old approaches 40 in February but continues to score at an impressive rate with 74 goals in 83 matches for Al-Nassr.
Despite his age he can still display a variety of finishes as his bicycle kick against Poland in November showed.
The Club World Cup gives the Saudi Pro League another opportunity to globalise their product as they aim to develop from a retirement home for stars to a group of world class teams.
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Teams within the league have been able to offer life-changing contracts to stars towards the end of their careers, including Karim Benzema and N'Golo Kante.
Former Brentford striker Ivan Toney signed a reported £400,000 per week contract with Al-Ahli, numbers which may attract an inform 32-year-old Salah.
"Every side will be strong and is excited to play in this tournament. No one is going to be easy at all," said Calzada.
"This tournament gives us the opportunity to test our level. We have put together what we believe to be a very strong team. It has been very dominant locally. We are very keen to see what will happen when we play the greatest teams in the world.
"We plan to come to this tournament with the biggest ambitions."