Vinicius made his first appearance for the Selecao in Tuesday's underwhelming 1-0 defeat to Peru, Brazil's first loss since last year's World Cup.
The 19-year-old has started 10 LaLiga matches across the past two seasons, too, and Casemiro believes he needs to be aiming high.
"Vinicius has a very good head and, in the past year, he has surprised many people with the football he played," the midfielder told reporters.
"It is not normal for a 19-year-old boy to do what he did with the Real Madrid shirt. I told him the other day that this year is a year that he has to start thinking big.
"I repeat: what he did last year was not normal. He surprised everyone and showed that he is ready to be a starter at Real Madrid.
"When you are a starting Real Madrid player, you have to think big. Think of the Ballon d'Or, FIFA's World XI. He is a great player and he has already proven it.
"Of course, he is very young, you cannot put too much pressure and weight on his back. But I think he has to start thinking big.
"It is very important for us that he is here with the national team, but we have to be calm; two years ago he was playing in the Flamengo youth team."