"Arriving early in Paris for treatment. The MRI scan shows a torn ligament from the fall in Roma," the 2014 French Open finalist said.
"I'm keeping my fingers crossed for RG (Roland Garros) and will do everything possible to be ready. Doctors say it's 50/50 at the moment but it's made good improvement since Sunday.
"We are remaining very positive."
With Serena Williams, Victoria Azarenka and Maria Sharapova all absent, Halep would be one of the favourites to claim what would be a maiden grand slam crown at the May 28-June 11 tournament.
She won the title in Madrid and looked on course to follow that triumph in Rome but stumbled early in the final against Ukraine's Elina Svitolina and went on to lose in three sets.
(Reporting by Martyn Herman; Editing by John O'Brien)
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