The 49-year-old was part of the Brazilian side that won the Japan/Korea 2002 World Cup title.
He also claimed that during his prime, he was better than Messi and Juventus star Cristiano Ronaldo.
Similarly, Edilson said compatriot Neymar has to win the competition to be better than him, insisting that he was more skillful than the trio.
Messi and Ronaldo have won 11 of the last 12 Ballon d’Or and have a number of individual prizes to their names.
But Edilson, who played for Palmeiras and Corinthians in his home country and was never nominated or won the Ballon d’Or, stressed that his World Cup medal gave him an edge over them.
“At my best, I played better than Neymar,” he was quoted as telling TV Bandeirantes.
He added, “He (Neymar) 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.”
For Ronaldo, Edilson believes the Portuguese is good with both feet and has strength but still does not match his skills.
Messi played the final match of the 2014 World Cup with Argentina where his side lost narrowly to Germany one to nil in Brazil.
Ronaldo and Neymar have also made it to the semi-final of the competition with their respective nations.