The report in Folha de S.Paulo did not say how it obtained the information and was dismissed by World Cup officials in the city.
Reginaldo Cordeiro, Curitiba's World Cup secretary, denied the story and FIFA executive committee member Jim Boyce, who is also a member of the World Cup Organising Committee, said he was unaware of any developments aimed at taking games away from Curitiba.
"No, no, no, this comes from a declaration made by (head of the Local Organising Committee) Ricardo Trade when he was asked by a newspaper in Brasilia if the alternative to Curitiba's Arena da Baixada would be Gremio's ground (in Porto Alegre)," Cordeiro told Reuters.
The two cities are around 460 miles part.
"Trade replied saying if there was to be an alternative the games would go elsewhere, but not Gremio," Cordeiro added.
"It's rubbish. Curitiba has not been counted out."
Cordeiro said FIFA's stadiums manager Charles Botta returns to the city next week to finally rule on whether Curitiba will be included in the competition. FIFA wants a decision by Feb.18.
Boyce said that as far as he was aware, FIFA had not issued Curitiba with any ultimatum and was still planning on matches being played there as scheduled.
"Obviously we have certain issues with Brazil's preparations for the World Cup and I know that Secretary General Jerome Valcke is spending two weeks in every month there," Boyce told Reuters.
"However, I have had no correspondence at all regarding plans for a change of the venue from Curitiba, but this issue and everything else will be on the agenda when the World Cup Organising Committee meets in Zurich on March 18 and any decision will be discussed by the executive committee on March 20 and 21."
Four matches are scheduled to take place at the 41,500-capacity ground, Iran v Nigeria on June 16, Honduras v Ecuador on June 20, Australia v world champions Spain on June 23 and Algeria v Russia on June 26.
The stadium is not being used after the opening group stage.
FIFA wants to know by Feb. 18 whether it will be ready or not because representatives from the 32 finalists are meeting that day to discuss planning and logistics.
However, the stadium is way behind schedule and possible alternatives include Porto Alegre, Sao Paulo, Rio de Janeiro and Belo Horizonte, all of which are close enough to ensure teams who have based themselves in the south are not hit with long flights to games.
Six of the eight teams due to play in Curitiba will be based either in Parana state, of which Curitiba is the capital, or neighbouring Sao Paulo state.
Officials who have worked on the stadium's financing say construction work fell behind schedule because the club that owns it, Atletico Paranaense, chose to build the stadium themselves rather than hire an established construction firm.
The club has had trouble getting financing for the job and yesterday the state stepped into solicit a new credit line of up to 65 million reias (£16 million).
The money will be used to finish the job, state government officials said.
The original cost of the stadium was set at 131 million reais (£32 million) but it has since risen to 319 million reais (£79 million).
The delay is the worst of all the 12 stadiums due to be used in the World Cup, the first to take place in South America since 1978.
Five of the 12 stadiums are not yet finished, even though the deadline was last December.
The Arena Corinthians in Sao Paulo, where the prestigious opening match is due to be played on June 12, will not be ready until less than two months before the kick off.
Football's governing body has never excluded a venue so late in the day and if it did so now it would face a logistical nightmare.
Both FIFA and Brazil would face embarrassing accusations of ineptitude, as well as a potential avalanche of law suits from fans who have bought tickets, hotels or flights to stay in Curitiba.