The clay-court Slam is set to get underway on Sunday, May 24 and end on Sunday, June 7 but is now in question along with the other upcoming events on the tennis tours.
With the event considered the unofficial fifth Grand Slam, Indian Wells, having already been cancelled due to the outbreak of the virus, there is now considerable speculation about the clay-court season across Europe.
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Speaking to L'Equipe, Forget said the year's second Slam would simply have to follow the recommendations from the French government and medical experts.
"Inevitably, the tournaments scheduled for the coming weeks are all exposed. Organized behind closed doors? It would also be a problem," Forget said.
"Would it be economically viable? By the time of Roland-Garros, there is time left but at the same time things will move will happen quickly.
"I think, first and foremost, of the health of the players and spectators.
We will explore all the possibilities but, in any case, the decision will not be up to the French Federation. We will follow the recommendations.
"The big unknown at the moment is how long it will last."
France on Sunday temporarily banned all gatherings of more than 1,000 people in a bid to curb the spread of the coronavirus.
French authorities had earlier banned gatherings of more than 5,000 people in confined venues.
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