The Real Madrid winger lauded his Argentina team-mate for his four goals in three World Cup games and insists the team spirit in the Albiceleste camp is second to none
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Messi started slowly in the Albiceleste's opener versus Bosnia-Herzegovina before bursting into life by scoring the eventual match-winner, and he did the same again when they defeated Iran 1-0 in their second game.
An impressive double in the final group game saw him rocket to the top of the Golden Boot tally - though he has since been overtaken by Colombia's James Rodriguez - and Di Maria is confident his captain will emerge on top.
"Messi is the best in the world," he told Marca. "What he does nobody else can do and luckily he's ours.
"He is going to be the World Cup's big goalscorer. He's at a tremendous moment and that's very good but we all catch it off him."
Argentina managed narrow victories in each of their group games but, ahead of Tuesday's clash with Switzerland, Di Maria claimed that team spirit is high and he expects them to be in the final come July 13 should they up their game in the knockouts.
"We're going from a lower level to a higher one. We haven't reached our best level yet, but I still believe we can win the World Cup," the 26-year-old said.
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"The emotional bond that we have here is fundamental. There is zero friction and during these days living together, we are more united than ever. We feel very strong.
"We knew that our rivals were going to fall back and that we would get the space to play our game."
Argentina, should they beat Switzerland, will face Belgium or USA in the last eight of the tournament.