French Open director Guy Forget said he was working hand in hand with tennis authorities to make sure the dates of the claycourt Grand Slam tournament and those of the US Open do not clash, adding that Flushing Meadows would make an announcement next month.
The French Open had originally been due to start on Sunday, but the new coronavirus crisis forced organisers to postpone the start to Sept. 20, one week after the scheduled final of the US Open, leading to criticism within the tennis world.
Earlier this month, the French tennis federation said it was in talks with the ATP, WTA and the International Tennis Federation (ITF) over a revised calendar for the season.
"The official announcement has not been made yet. It (the French Open) will probably be between the end of September and the beginning of October. We've been working closely with the ATP, the WTA and the ITF to make a global announcement on what the circuit will be like until the end of the year," Forget told French radio Europe 1 on Saturday.
"There are so many question marks. The city of New York is more affected by the coronavirus than France. They also have a lot of organisation problems, they will make an announcement mid-June to say how it's going to be like for the US Open."
Meanwhile, Forget is confident the French Open will be played in good conditions.
"We'll see how the situation is in a couple of months. We will adapt to what the government will say. We have to be ambitious and optimistic," he said.
France has banned events involving 5,000 or more people until the end of August.