The Brazilians are also considering dividing the huge country into four regions, in which teams would be confined during the earlier rounds, to cut down on travelling.
Sao Paulo's plans were thrown into confusion last month when the committee and world governing body FIFA dropped the proposed venue, the Morumbi stadium, because the city had failed to provide financial guarantees for the renovation of the arena.
"If Sao Paulo wants to host the opening game or the competition as a whole, the deadline is getting close," Teixeira told reporters.
"Cape Town built its stadium in two-and-a-half years, so we are dangerously close to the limit."
"Nothing has been determined, it was a generic conversation because he (Kassab) is on holiday at the moment," said Teixeira.
"When I return to Brazil and he comes back from holiday, we will have a meeting with the governor of Sao Paulo."
"Brazil is a continent not just a country, so we may divide it into four pieces, to make sure that fans do not have to travel (fly) more than one or two hours from one stadium to the other."
"Next month, we will have the reports of the financial analysis of the stadium projects and we will see whether there is a problem or not," he said.
"Airports are the responsibility of a government department called Infraero," he said.
He dismissed fears over Brazil's soaring crime rate, saying that violence happened everywhere.
"This problem exists all over the world. I see violence wherever I go, in Europe, in the United States, and in Brazil it's not different," he said.
