The threat brought an angry reaction from stadium owners Corinthians, who said FIFA were welcome to move games if they wanted to and said they would not tolerate any pressure.
FIFA Secretary General Jerome Valcke said that football's governing body would not accept any failure to meet the December deadline for the completion of the Itaquerao stadium, which is due to stage six World Cup matches including the opening game.
Constructors have already warned that the stadium will not be ready until the end of February.
"We have said clearly that delays are not possible for the World Cup," Valcke told reporters in Brasilia after visiting the Mane Garrincha stadium, which will be used for both next month's Confederations Cup and the World Cup.
"We are going to discuss the situation in Sao Paulo very firmly," he added, suggesting that FIFA could transfer matches elsewhere.
"We can change everything until the tickets start to be sold, which gives us until August 1 to change the stadiums."
Corinthians, who do not currently have their own stadium, had originally planned to build a 48,000 capacity arena but agreed to add another 20,000 temporary seats to accomodate next year's World Cup.
The club said FIFA had agreed to give them an extra two months after work on the stadium was delayed by bureaucratic difficulties.
"If FIFA understand that they have to move the venue for the opening game, then they can be our guests," said the club.
"The situation set out by Valcke today seems a bit strange to Corinthians as... the deadline was extended by Valcke himself until February 2014.
"The aim of Corinthians has always been to serve the city, the state and the country. That's why the club increased the capacity of the stadium and we will not accept any type of pressure."
Valcke upset Brazilians last year when he said the country needed "a kick up the backside" following numerous delays in preparations.
Four of the six stadiums which will be used at the Confederations Cup over-ran the deadline for completion but FIFA has emphasised it will not allow similar delays before the World Cup itself.
Sao Paulo authorities had initially planned to used the Morumbi stadium for the World Cup but this was ruled out in 2010 due to a lack of financial guarantees for the reconstruction.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
