Sao Paulo is scheduled to host six World Cup matches, including the opener and one of the semifinals, but Valcke said that organizers "have to speed up."
"And don't forget, and it's not a threat, we can change all until the first minute of the ticket sales," the Frenchman said during a visit to the new stadium in Brasilia. "So we can change all the match schedule until the first of August."
Engineers in charge of Sao Paulo stadium construction said last week it will be not ready by December as FIFA wants.
Valcke said FIFA won't tolerate delays with the 12 World Cup stadiums. Only two of the six venues for the Confederations Cup — a warm-up tournament to be staged this year — were completed on schedule. Brasilia, which hosts the first game in the Confederations Cup on June 15, is to hold it first official match on Saturday.
"I think we have been clear," Valcke said. "There will be no delay. No way that we can accept any delay for the World Cup 2014. Because as you will see for the World Cup we need a lot more time to install all the facilities for the media, for the hospitality, for all of what we need in order to deliver the World Cup.
"The World Cup is again another event than the Confederations Cup. So there will be a discussion with Sao Paulo about their stadium. We will have to sit down and see exactly what's happening. And we told them already that they should speed up. Whatever it means for them, they have to speed up."
Brazil was awarded the World Cup in 2007 but was slow to get going on construction. It has faced a torrent of criticism from FIFA during the past year, with Valcke doing most of the criticizing about the delays.
The main concern in Sao Paulo is the temporary seating needed to increase the stadium's capacity for the opener. Twenty thousand seats will be added after the stadium's main structure is ready, increasing the capacity to nearly 70,000.
The company building the stadium, Odebrecht, has told The Associated Press that it will finish the main structure with 48,000 seats by the December deadline. But chief engineer Frederico Barbosa says it will likely take more time to add the temporary seats, which could only be ready by February or March.
Valcke will visit Rio de Janeiro's Maracana stadium on Wednesday. The newly renovated venue will host its first big match on June 2 — an international friendly between Brazil and England. It will also stage the Confederations Cup final on June 30.