The Fifa general secretary Jerome Valcke says the pressure is on Brazil to be ready to host this year's World Cup and Curitiba risks being dropped as a venue if work on the stadium fails to make significant progress.
Valcke made the comments during an inspection tour of Brazil, where some of the 12 stadiums remain unfinished.
Curitiba is set to host four group matches, including the meeting of holders Spain and Australia.
The World Cup will start at Sao Paulo's Corinthians stadium on June 12th with a match between Brazil and Croatia.
Two workmen were killed at the venue as a crane fell and destroyed parts of stadium last November.