The Arena da Baixada has become a particular cause of concern for football's governing body as work is alarmingly behind schedule, with a matter of months to go before the World Cup kicks off.
Valcke is currently undertaking a tour of all of the host cities, with a number of stadiums not yet completed.
But his fears for Curitiba have led to the formation of a technical committee - involving FIFA, the Local Organising Committee, the local authorities at Curitiba city hall, the Parana state government and home club Paranaense - which will undertake an evaluation of the site in three weeks and use those results to decide whether the city will remain a host.
Valcke told a press conference: "To be very honest, the situation as it stands is not ideal.
"The stadium is very delayed and well outside the delivery schedule to ensure best use by FIFA and the FIFA World Cup.
"But we have to be positive and that's why we have come together, as the main driving forces involved, to find solutions.
"By February 18, the date of the Team Workshop in Florianopolis where all 32 qualifying sides will be given important information about the FIFA World Cup, we have to decide between us - the city of Curitiba, the state of Parana, Clube Atletico Paranaense football team, the LOC and FIFA - whether the stadium is in a position on that date to give us the confidence to hold World Cup matches there, without risking the organisation of the event.
"We will have people from FIFA and the LOC monitoring the stadium's progress on a daily basis and we will work together to guarantee that Curitiba will host FIFA World Cup games."
Curitiba has been earmarked to host four group stage matches, including defending champions Spain's clash with Australia on June 23.