The former Brazil midfielder believes the Argentina captain can only be considered one of the greatest to play the game if he makes a decisive difference in the knockouts
The Barcelona forward has inspired the Albiceleste so far in Brazil, scoring four times in the group stages to lead the Golden Boot standings alongside Neymar and Thomas Muller.
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"If Messi cannot make a difference in a World Cup, as in the past Pele, [Johan] Cruyff and [Diego] Maradona, he will never arrive at their level," the 44-year-old told Corriere dello Sport.
"He has already won more trophies and Ballons d'Or than all of them. But only a triumph at the World Cup makes you enter the Olympus of football."
Leonardo, who was a World Cup winner with Brazil in 1994, does not rate Argentina's chances in the tournament, instead backing his compatriots to win their sixth crown should they overcome last-16 opponents Chile.
"Brazil are favourites," the former AC Milan player claimed.
"[A Brazil-Argentina final] would be fascinating to the eye but Germany [who are in Brazil's half of the draw] are very solid.
"Brazil's first two games have been played with an exaggerated worry and tension that has affected the play of a team inexperienced at World Cups. The squad is not yet as solid and concrete as it should be, but it is growing.
"Brazil is favoured by tradition and by the fact they are playing at home, but on the field we are not so superior. Chile has fighters as well as two world-class players in Arturo Vidal and Alexis Sanchez."
Chile and Brazil meet in Belo Horizonte for their last-16 encounter on Saturday.