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Messi outshone his Argentina's teammates Gonzalo Higuain, Sergio Aguero and Di Maria during the group stage of the tournament, scoring four goals in the 4-3-3 system currently favoured by coach Alejandro Sabella.
The Barcelona star has regularly spoken about how he wants the team organised in this 4-3-3 shape.
And Di Maria is happy to accommodate Messi, telling Marca that he and his teammates were lucky to have a player like Messi in such great form at the moment.
"It suits us if there is movement of the ball, above all in the final 30 metres, because with the way we play we can arrive with more players and well positioned," Di Maria said.
"We all have to help Leo. The important thing is to do my work for the team. He is the best in the world. What he can do nobody else can, luckily he is ours. Messi will be the World Cup's top scorer.
"He is in tremendous form. And that is good for us, as it rubs off on all of us. We are improving. We have not reached our level. But I still think we can win the World Cup. There are no strains within the group. These days we are more united than ever. We feel very strong."
Di Maria accepted that Argentina had found it difficult to create chances during their opening two group games against Bosnia and Iran, but predicted Switzerland would be more positive tactically, leading to extra space for the Albiceleste attack to exploit.
"We knew that our [group stage] opponents would stay back and not give us space to play our game," he said. "[Switzerland] will be different, because they come out to play. They have good midfielders and forwards, but are not as solid in defence.
"We have to keep improving in our play, and think about ourselves. It will be a more open game, like Nigeria [in their final group game]. We must be focused on not making any mistakes, because at this stage you can be left out of the competition."
Asked about how the 4-3-3 shape requires him to run constantly to help out in both attack and defence, Di Maria said he did not get tired on the pitch but after games he was often so exhausted he could not speak.
"I am always running," he said. "And I do not stop until I get to the dressing-room. On the pitch I never get tired because I want to give my all, but I feel exhausted when I get to the dressing-room. Then I do not have the strength even to talk. I want to play always and help Argentina to continue in the World Cup."
Di Maria was not however asked about speculation that he could be sold by Real Madrid this summer, to raise funds and make room in the squad for a big-money move for emerging world star James Rodriguez of Colombia and Monaco.
Last summer saw similar rumours ahead of Gareth Bale's arrival at the Estadio Santiago Bernabeu, however Di Maria stayed and played a key role in the finals as Madrid won the Champions League and Copa del Rey.
Meanwhile, Ottmar Hitzfeld has told his Switzerland team they can "write a page of history" with victory over Argentina in Tuesday's round of 16 encounter.
The Nati have not reached the quarterfinals of a World Cup since they hosted the tournament in 1954. However, having shaken off their 5-2 group-stage thumping by France with a 3-0 defeat of Honduras to end their Group E campaign, the Swiss head into the match in Sao Paulo in buoyant mood.
That optimism is symbolised by Hitzfeld, 65, who will end his glorious coaching career with elimination in Brazil.
The former Borussia Dortmund and Bayern Munich boss believes his well-laid retirement plans will be put on hold a little while longer.
"From now on, everything is down to a single match during which anything is possible. That means we have no pressure on us at all," Hitzfeld told media at his prematch news conference.
"I'm convinced that we'll create chances against Argentina. We're the outsiders, but we don't impose any limits on ourselves. Swiss football can write a page of history. It's the time.
"My players could experience one of the greatest moments of their career. And I do not start with the thought that this will be my last match. On the contrary."
ESPN FC's France correspondent Ian Holyman contributed to this report.
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