Lamine Diack, the former president of world governing body the IAAF, is already being investigated by French authorities.
He was arrested last year on corruption and money laundering charges, over allegations he took payments for deferring sanctions against Russian drugs cheats.
Confirming the investigation was being widened, an official from the prosecutor's office said: "We are looking at these elements, but at this stage it is a question of verification. Nothing has been proved."
The International Olympic Committee (IOC) has told the BBC it wants to be a party to the French investigations.
Tokyo, which will host the 2020 Olympics, defended the voting process when it came under scrutiny in January.
And Rio 2016 organisers said on Tuesday that the city "won the right to host the Games because it had the best project".
"The difference in the votes, 66 to 32 against Madrid, excludes any possibility of an election that could have been rigged," communications director Mario Andrada said.
