The Germany international is yet to be on the losing side against the Argentina star and is hell bent on extending that record this weekend
Muller has enjoyed another stellar World Cup, with his five goals in six games matching the tally that won him the golden boot four years ago in South Africa.
And the Bayern Munich man says he and the rest of the team will do everything in their power to lift the trophy for the first time in 24 years.
"It'll be very important to push ourselves to the limit, especially defensively. You need to be quick to keep up with [Lionel] Messi.
"We've played against Messi a few times. I've never lost a competitive game against him.
"We haven't had a tour of Rio de Janeiro yet but for me the only reason for going back there is to win the World Cup."
Germany thrashed hosts Brazil 7-1 in the semi-final but Muller expects Sunday’s clash at the Maracana to be a much stiffer test for Joachim Low’s side.
"I don't know what kind of a game it will be on Sunday, but I don't expect it to be 5-0 at half-time," he said. "That would be nice, but it's probably going to be tight like it was against Algeria or France."
"We'll give everything we've got to win the World Cup.”