Casemiro joined United in a potential £70 million deal last week from Real Madrid, where he was previously a teammate of Ronaldo's for several seasons. And Casemiro said Ronaldo has already helped with the transition to his new surroundings.
"We are talking about one of the best players of all time," Casemiro said in an interview with ESPN Brasil. "He knows that I respect him a lot. I hope he stays with us, because he is a great player.
"He gives you a lot of goals, he is a winner, he is a leader. He is so important for us. We approached each other because of the language, too. Since the first day here, he has helped me with everything. He is helping me a lot. I really hope he stays with us."
Ronaldo was left on the bench as Man United secured their first win of the new season with an impressive 2-1 victory over Liverpool on Monday. That followed weeks of speculation after reports that the 37-year-old wanted to leave to join a club in the Champions League.
However, United have continued to say that the player is not for sale and after the Liverpool game, manager Erik ten Hag reiterated his stance that Ronaldo can thrive in his system.
"I think he can," said Ten Hag who brought Ronaldo on as a substitute in the 86th minute. "The whole of his career under several managers he did, several styles and systems. He always performed, so why can't he do this?
"His age is not an issue. If you are good enough and you're old and you still deliver performances, you are also good enough."
Casemiro's move to Old Trafford was a surprise to many, with the Brazil midfielder leaving the current Champions League holders for a club that finished sixth in the Premier League last season.
But the 30-year-old has stressed he is eager and ready for a new challenge after nine years in Madrid.
"As I said in my farewell at Real Madrid, I felt that it was an end of a cycle," he said. "I had the sensation that I gave everything for that club. I'm 30 years old, I'm feeling so strong. I want to learn a lot. I want to learn new things. I want to change.
"If it had happened three years ago, maybe I wouldn't have this desire to change. But I'm still 30 years old. So, this desire is too good for me. I'm feeling like a boy. I want to help, I want to play, I want to help the players. I want to help Manchester United."
And despite United not being in the Champions League this season and having not won the Premier League title since 2013, Casemiro insisted he still has ambitions to challenge for the game's biggest trophies.
"Well, I have five [Champions League's], right?" he joked. "But, it's not because I have five that I don't want to win with Manchester. The Champions League is the most important championship and everyone wants to win it.
"But, as I said, the club was very nice with me since the first day, the coach as well, they left me very comfortable... These things are important. And sure if we will not be at the Champions League or win the Premier [League], I will be sad, very nervous. But we know it happens with a lot of work and dedication."