Gilbert Ysern, general director of the French tennis federation, told a news conference on Saturday that relocating the clay-court Grand Slam from Roland Garros is being considered because it needs more space to remain competitive with the three other major tournaments.
Three options are being examined, including one next to Versailles castle. Another possible site is near Disneyland Paris.
The French Open has been at Roland Garros since 1928 and the federation has a contract there till 2015. The French federation assembly is expected to make its decision in February.
"I think by the time I finish my career, the tournament will still be at Roland Garros," Federer said. "I don't know if the French Open will one day move to Disney, I doubt it. There is more space outside the city, I understand, but come on ..."
Henin accepted that space is an issue at Roland Garros, but said its tradition is one of the French Open's main assets.
"I hope they find a solution to keep the tournament here," she said. "The tradition is here. This is my favorite tournament. Maybe (a move outside Paris) will happen. You need to be realistic. Compared to other Grand Slam tournaments, which are always getting bigger, it has become difficult in terms of space. Everyone knows that."
Among the Grand Slam tournaments, only the French Open and Wimbledon have never been moved. While Wimbledon has been updated, facilities at Roland Garros have become outdated. The lack of space for 450,000 annual spectators, players, journalists and sponsors is a problem, while the absence of covered courts leaves the tournament vulnerable to the weather.
"We have to create the Roland Garros of 2040," French federation vice president Bernard Giudicelli said. "We will do everything to make sure that Roland Garros 2016 will be played in a bigger and modernized stadium."
The French Open's facilities are spread over 21 acres, while Melbourne Park — the site of the Australian Open — and Wimbledon each have 49 acres. Flushing Meadows, site of the U.S. Open, has 34.5 acres.
"Some players told us they cannot imagine leaving Paris," Ysern said. "But if we stay, we have to modernize the facilities to aim for excellency. We need more space and a retractable roof over the center court."
Jo-Wilfried Tsonga said there is only one Roland Garros.
"I would prefer to stay here and make the tournament bigger here because this site is wonderful," Tsonga said.
If the tournament stays in Paris, three adjoining areas will be added to Roland Garros at a cost of about $251 million. Building a new stadium outside Paris would cost an estimated $754 million.
Versailles castle is 12 miles from downtown Paris. Disneyland Paris in Marne-La-Vallee is 30 miles from the French capital.
Should the tournament be relocated, preliminary designs envision a 74-acre site with 55 tennis courts — two with a retractable roof — that would be able to receive up to 60,000 people a day.