Opposition groups, calling the dead protester a "F1 martyr", claimed the latest clashes with police resulted in a body being left on the roof of a building less than 10 kilometers from the capital Manama.
Sky News in Britain said the Kingdom's government declined to comment.
"We know protests can have a negative result," Frenchman Todt told the BBC when asked about the reported death.
"We are a governing body running sport, you can have lots of protests and there can be consequences, and I am not sure the protests would not have happened if the grand prix would not have happened."
The FIA president said all the teams support the Bahrain grand prix.