The Brazilian city faces the prospect of losing its status as a World Cup venue, with FIFA secretary Jerome Valcke describing the situation as reaching a "critical point" ahead of a revised February 18 deadline.
Stadiums for the tournament were supposed to be completed by December 31 and Valcke suggested that the four group matches set to be held in Curitiba could be moved unless "rapid progress" is made by the next FIFA visit.
Australia are due to play defending champions Spain in Curitiba in the final Group B game on June 23, and the FFA plan to talk to FIFA in order to safeguard the interest of supporters.
"FFA has noted FIFA's comments that Curitiba's World Cup stadium is only 90 percent complete and missed the initial December 31 deadline and will seek advice from FIFA on the issue," an FFA spokesperson said.
"The prospect of matches being moved from Curitiba raises serious concerns, particularly for Socceroo fans who have secured tickets and made flight and hotel bookings.
"We hope the measures announced will ensure that Curitiba's readiness will be confirmed by the 18 February deadline."
Curitiba is also due to host the matches between Iran and Nigeria, as well as the contests between Honduras and Ecuador and Algeria and Russia.
