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|People hold their umbrellas in the empty stands as rain falls on Court Philippe Chatrier in Paris, France. (AFP/CHRISTOPHE ARCHAMBAULT)|
Tournament director Guy Forget said he remained hopeful of the French Open finishing on time on Sunday.
However, if the weather continues to deteriorate, the women's final could be shifted from Saturday to Sunday, sharing top billing with the men's title match.
"We always have to study the worse case scenario," said Forget.
Wednesday was the second time since 2016 that all Roland Garros play was cancelled and third since 2000.
The decision left world number one Novak Djokovic and defending women's champion Simona Halep to play their quarter-finals on Thursday and semi-finals on Friday if they get through.
With the women's final traditionally set for Saturday, third seed Halep could end up playing three days in a row.
"The weather for tomorrow seems to be OK but Friday is already looking complicated," added Forget.
Thursday's schedule has been brought forward by two hours to accommodate Halep's quarter-final against American teenager Amanda Anisimova and Djokovic's last-eight tie with Alexander Zverev on Court Philippe Chatrier.
On Court Suzanne Lenglen, America's Madison Keys was due to face Australia's Ashleigh Barty before 2018 runner-up Dominic Thiem clashed with Russia's Karen Khachanov.
Friday was originally set to stage both men's semi-finals for which Rafael Nadal and Roger Federer had already booked their places on Tuesday.
Johanna Konta and Marketa Vondrousova had been due to play their semi-final Thursday but that has already been shifted to Friday.
"We don't want to move the women's final from Saturday to Sunday but some girls may be playing three days in a row," said Forget.
"These girls have been waiting all of their lives to play such a match of this magnitude.
"If we have to move the finals to the following day it's something that could happen. We have done it with the men (Rafael Nadal v Djokovic final of 2012).
"It's not what we hope but if we have no other choice then that's what we will do."
Forget said it was possible that one of the women's matches could be moved away from the Chatrier and Lenglen courts to the 5,000-seater Simonne Mathieu arena.
"You are always afraid that some players may think it's a lack of respect or we have diminished it.
"But we want to see players in the best possible condition and if we have to make the tough call to move players to a smaller court, it's a possibility," said Forget.
Djokovic has fallen foul of the weather in Paris before.
In the 2012 final against Nadal, he dropped the first two sets before winning the third and was 2-1 up in the fourth when play was suspended until Monday.
But on the resumption, Nadal reimposed his authority and won in four sets for what was his seventh Roland Garros title.
In 2020, the French Open will be less affected by the vagaries of the weather as a retractable roof over Chatrier will come into operation.