The project was agreed on earlier this year and an architect was appointed but the Paris City Council is now getting cold feet, FFT director general Gilbert Ysern said.
"It seems that the mayor's entourage has become more hostile to our project - which was not the case when we launched it," Ysern said.
"Add to that the residents' opposition and we are now forced to look for other options, including that of leaving the premises."
Last May, tennis officials said a new centre court equipped with a retractable roof would be used at Roland Garros for the French Open by 2013 or 2014.
Of the four grand slam events, the Australian Open has two courts with a roof, while Wimbledon's Centre Court unveiled its new translucent retractable roof this year.
Paris City Council and the French government were set to invest £18 million each in the project which is estimated to cost £160m.
Officials at Paris City Council could not be immediately reached for comment.