"We are thinking about it, we have several elements that encourage us to investigate," Houlette told French radio Europe 1.
The financial prosecutors can investigate if they have reasons to believe French nationals are involved in a case or if unlawful acts related to it were committed in France.
Former UEFA president Michel Platini, banished from the sport for ethics violations, could be a person of interest.
"If there is an investigation, Mr Platini's role will be crucial but the investigation would not focus on Mr Platini," said Houlette.
Platini was banned for four years over a payment of two million Swiss francs ($2.08 million) made to him by FIFA with former president Sepp Blatter's approval in 2011 for consultancy services provided a decade earlier.
(Reporting by Julien Pretot; Editing by Clare Fallon)
