The Swiss advanced to the last 16 courtesy of a 3-0 win over Honduras on Wednesday, which featured a hat-trick for Xherdan Shaqiri.
That victory saw Ottmar Hitzfeld's side set up a clash with Argentina in Sao Paulo on Tuesday.
And Benaglio is hoping Argentina's fierce rivalry with tournament hosts Brazil will work in Switzerland's favour.
"We will have the support of the Brazilian fans in the stadium," he said in a press conference on Friday.
"One can feel the rivalry between Brazil and Argentina.
"It would be nice if it were a Swiss home game."
Argentina's talisman and captain, Lionel Messi, has played a crucial role in his team's progress thus far, scoring four times in three matches to top the goalscoring charts along with Brazil's Neymar and Thomas Muller of Germany.
And Benaglio concedes it is difficult to anticipate what a player of Messi's quality will do before a game.
"We're preparing for him as we would any other player," he said.
"But it is also clear that it will be difficult to take Messi out of the game completely.
"You can watch as many videos of Messi but when he makes something surprising at the crucial moment, it will have been to no avail."
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