"What is certain is that he will not be there for the Nice game (on Wednesday). For Sochaux (on Saturday), it will be difficult and after that, we will have to wait and see", Blanc told reporters.
"The medical staff will let us know."
Gourcuff, France's first-choice playmaker for the World Cup, picked up the injury on April 24 in a 1-0 Ligue 1 defeat at Lorient.
He was replaced at half time although he picked up the injury early in the game.
Blanc, however, said he would not force his player to resume too soon, as France coach Raymond Domenech is set to unveil his 23-man squad for the World Cup next Tuesday.
"I will not take any risk," he said.
"But if he is fit, it means he is able to be in the (Bordeaux) squad, to play a game, to start a game.
"But today he only had a little jogging session so we're not there yet."
France were drawn in Group A with hosts South Africa, Uruguay and Mexico in the World Cup that starts on June 11.
