Edilson helped the national team win the 2002 World Cup and also claimed four Brazilian league titles with Palmeiras and Corinthians.
"At my best, I played better than Neymar," he told TV Bandeirantes. "He needs to win the World Cup in order to be better than me.
"I have personality, and for Messi to be better than me, he also has to win the World Cup.
"Cristiano Ronaldo is just strength; he strikes the ball well with both feet, but I'm more skillful than him."
However, Ronaldo captained Portugal when they won the European championships in 2016, while Neymar scored the winning penalty to secure Brazil the Olympic crown four years ago.
Brazil also won the Copa America on home soil last year, but Neymar missed the tournament due to injury.