"We will make our decision public on Facebook on May 16 at 1900 (local time, 1700GMT)," French federation president Bernard Giudicelli told a news conference on Wednesday.
"There is no reason why we should make an exception for Maria Sharapova. There is no reason why we should announce a wild card before the others."
Giudicelli said he will discuss the matter with tournament director Guy Forget on May 15.
Former world number one Sharapova, 30, is returning to action on Wednesday from a 15-month doping ban after being awarded a wild card for the Stuttgart claycourt tournament.
"The tournament is bigger than the players," added Giudicelli, who said he would call Sharapova before the decision is made public.
With 23-time major champion American Serena Williams already out of the picture because she is expecting a child, the tournament would be deprived of the other big name of women's tennis if organisers decided not to invite Sharapova, a two-time French Open champion.
Giudicelli, however, said this would not be a factor.
"This is not a cast. This is not a rock opera," said Giudicelli.
Sharapova's invitation for the Stuttgart tournament raised eyebrows in the tennis community, with Romanian Simona Halep, who was defeated by Sharapova in the 2014 French Open final, saying: "For the kids, for the young players, it is not OK to help with a wild card the player that was banned for doping.
"It is not about Maria Sharapova here, but it is about all the players that are found doped."
Women's Tennis Association chief Steve Simon defended Sharapova, saying she does not need to be punished more.
(Editing by Sudipto Ganguly and Hugh Lawson)
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