Neymar has developed into one of the Liga champions' undisputed star players since joining from Santos in 2013 after a difficult start to life at Camp Nou.
He came third in the race for the 2015 Fifa Ballon d'Or - behind Messi and Real Madrid star Cristiano Ronaldo - and his compatriot believes there is more to come from the 24-year-old.
"I like Neymar a lot. He is a bit like me," Ronaldo told Calciomercato. "He had some difficulties in getting used to his new environment at first, but I knew that he was going to succeed.
"Can he be Messi's heir? Yes, he has everything he needs to become as strong as him."
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Ronaldo was a Barca player for one season in 1996/97 before eventually joining Madrid after a spell with Inter.
The iconic striker played alongside Zinedine Zidane at the Santiago Bernabeu side and he is confident the Frenchman can lead Madrid to Champions League glory this term having succeeded Rafael Benitez as head coach last month.
"Everybody knows that Zizou is a great friend. I really hope that he will have a great career as a coach too," Ronaldo added.
"He's the best player with whom I have ever played with. We had a lot of fun on the pitch.
"Could this be Real Madrid's year? Yes, they must focus on the Champions League, they have everything to succeed.
"Winning at Roma [in the first leg of their last-16 tie this week] was very important for Zidane."