Guy Forget doesn't sound too confident about the next few days:
The weather in Paris is forecast to be brighter on Thursday with a chance of a brief shower in the afternoon.
However, more rain is forecast for Friday which has led tournament director Guy Forget to "study worst-case scenarios".
One of the women's semi-finals could be moved to Court Simonne Mathieu if a decision is made to use Roland Garros' third show court alongside Chatrier and Lenglen in a bid to complete the matches.
Forget added it was possible the women's final could be pushed back to Sunday, with the men's final switching to Monday.
"It's not what we hope, but if we have no other choice, then that's what we will do," he said.