The forward suggested they share a level of self-belief unrivalled by other players, which has been one of the keys to their success.
"Outside the pitch, they are two very quiet people, but inside, they are two monsters.
"I heard Luis Scola [Argentinian basketball player] said both Leo and Cristiano enter the field convinced that they are the best and that is why they are the best. And I am sure that is so."
Dybala added that he is hoping to learn from the two icons:
"I can study them every day. Who doesn't want to play with the best? We are talking about two phenomenal players; two players who are one or two steps above the rest.
"They are at the top on a football level and also at a mental level. It is not easy to keep going and score 40 goals every year. It is crazy."
Ronaldo and Messi are still playing at 34 and 32, respectively, and many already consider them to be the two best players in the history of the sport.
Not many can rival their incredible achievements or astonishing numbers over the years.
In 817 club games, Ronaldo has contributed 607 goals and 213 assists for Real Madrid, Manchester United, Juventus and Sporting CP. That has helped his teams win 27 honours, including six league titles and five UEFA Champions Leagues.
Messi has spent his entire club career at Barcelona, where he has plundered 612 goals and 248 assists from 699 matches, resulting in 34 trophies. Of those, 10 are league titles and four are UEFA Champions League titles.
On the international stage, both players are their country's all-time scorer.
Ronaldo has 99 goals and 37 assists in 164 matches for Portugal, while Messi has 70 and 45 in 138 Argentina games:
The former's international career has hit incredible heights in recent years especially:
Ronaldo's efforts have helped Portugal win their first piece of major silverware. The Selecao won UEFA Euro 2016, although their talisman was taken off injured early in the final, and they also won the UEFA Nations League this year.
Messi won a gold medal with Argentina at the 2008 Olympic Games in Beijing, but despite helping La Albiceleste to a FIFA World Cup final and three Copa America finals, he has not won a trophy with his national team.
The heights they've reached over the years are extraordinary, but what perhaps separates them the most is the consistency with which they've done so.
They've been at the top of their games for more than a decade. Messi has scored at least 41 goals per season since he bagged 47 in 2009-10.
Ronaldo had enjoyed a similar run until last season, when he fell below 30 for the first time since 2008-09. Even then, most players would envy the 28 he notched for Juve in 43 games.
He hasn't been at his best this season—he's scored six goals in 14 appearances— either, but considering he'll be 35 in February, it's understandable he might finally be in decline.