Rodrygo, 21, has earned five caps for Brazil and is expected to make Tite's squad for the 2022 World Cup.
Like Neymar, Rodrygo began his career at Brazilian club Santos.
"Neymar said to me 'I'm already leaving the national team and the 10 is yours,'" Rodrygo told Podpah. "I didn't even know what to say to him. I was embarrassed, I giggled and didn't even know what to say properly. I told him that he must play some more, that I didn't want [him] to [do so] now. And then he laughed."
The iconic shirt has been graced down the years by Pele, Zico, Rivaldo, Ronaldinho and Neymar.
Neymar, 30, has scored 74 goals for Brazil and is within three goals of Pele's all-time record for Brazil.
Neymar is not the only football personality that believes Rodrygo is destined for greatness.
"[Former Real Madrid coach Zinedine] Zidane said that one day I would be the best in the world," Rodrygo said.
"[Real Madrid coach Carlo] Ancelotti also spoke about me. I try to train and evolve every day to get there. I was very happy. "I have this dream and I know that if I dedicate myself every day I can get there."
He scored nine goals in 49 appearances across all competitions this past season to help Madrid win LaLiga and the Champions League.