The Colombian is unable to envision the Barca legend teaming up with his great individual rival in Turin
Messi has sensationally told Barca he wants to leave the club, where the six-time Ballon d’Or winner has spent his entire professional career.
Though he has yet to explain his decision, Goal understands Messi intends to give his version of events in the coming days.
Others have suggested Messi could join Ronaldo in Turin to bring together the two best players of the modern day, but Cuadrado would be surprised if such a move happened.
“I can’t imagine it at all. The truth is that I don’t,” he told ESPN Nexo on Thursday.
Cuadrado added: “Just like with Cristiano, many people did not believe and suddenly he arrived.”
Man City is considered one of the most likely landing spots for Messi, with his former manager at Barca Pep Guardiola at the helm.
Goal has reported that Guardiola and Messi have spoken in recent days, with the pair still enjoying a strong relationship.
PSG could also be an option, with Messi potentially reuniting with former team-mate Neymar in the French capital.
Meanwhile in Turin, Juve are preparing to begin their 2020-21 campaign under a new head coach after Andrea Pirlo replaced Maurizio Sarri at the helm earlier this month.
Despite winning a ninth straight Serie A title, Sarri was dismissed after just one season in charge following his side’s Champions League exit to Lyon in the round of 16.
Cuadrado, who has been at Juve since 2015 and initially arrived on loan, said he was yet to hold talks with Pirlo about his plans.
“I have not had the opportunity to talk to him yet. When it is my turn I will surely tell him where I feel much more comfortable [playing],” he said.
“Hopefully what he knows and what a good player he was, he can contribute to the team and that we can get many titles together.”