French Open 2020: 'Optimism' that tournament will take place in autumn
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Andy Murray said last month he would definitely play on clay in September if the rearranged French Open goes ahead.
The French Open tournament director says there are grounds for optimism that the championships will be able to take place in the autumn.
The Roland Garros main draw was due to get under way on Sunday but has been postponed until September.
Guy Forget says he is not resigned to playing the tournament behind closed doors, and hopes to "welcome as many people as possible".
"At the moment, the signs are heading in a positive direction," he said.
"You can imagine that will also be the case for restaurants and bars in the weeks to come," Forget told the French radio station Europe 1.
"Now, we don't know what's going to happen in a month or two. We will adapt to whatever the government tells us.
"We should be ambitious and optimistic. We hope Roland Garros will take place, and under favourable circumstances."
The French Prime Minister Edouard Philippe has said no large sporting events will be allowed to take place in the country before September.
A start date of 20 September was initially announced by Roland Garros, but that is likely to be pushed back by a week or even two once the tours have considered their options.
"We are working very closely with the ATP, the WTA and the ITF so that we can make a comprehensive announcement about how the schedule will look from now until the end of the year," Forget continued.
"There are still so many question marks.
"The city of New York is even more affected by coronavirus than France. They also have some big organisational problems and will make an announcement around about mid-June to explain how the US Open will look."
There is very little chance of any tour events resuming before August. The US Open is due to begin on 31 August.