Joachim Low's side impressed during the group stages in Brazil, with forward Thomas Muller scoring four goals as Germany finished top with seven points.
Ozil has featured in all three matches so far and is confident that the three-time world champions can rewrite the history books.
Argentina, Brazil and Uruguay (twice) have won the World Cup previously when it was staged in South America, but the Arsenal midfielder thinks Germany can change that record.
"We can beat any team if we give our best," he is quoted as saying in Bild.
"We can become legends by winning the first European team in South America a world title.
"I will not fail (at a finals) again and have to wait four years to the next opportunity."
Low has used the 25-year-old in wider positions so far and Ozil is hoping to be given a chance in a more central role in the knockout stages.
"It is not easy (playing wide)," he added.
"Everyone knows that my favourite position is in the middle.
"From there I can do anything: to the right play, play to the left, directly forward play.
"Now I have to play differently."
Germany face Algeria in the last 16 on Monday in Porto Alegre.
