Organisers have been considering for years how to extend the current Roland Garros stadium, located on the leafy western edge of the French capital.
The projects, including the construction of a roof-covered court to avoid rain delays to the springtime clay-court tournament, have stalled, however, because of opposition, notably from the public and environmentalists.
"Over the last 10 years, the three other Grand Slam tournaments have progressed, notably in terms of infrastructure, but we haven't," tournament director Gilbert Ysern said, referring to the Australian Open, Wimbledon and the US Open.
"Roland Garros cannot stay the way it is," he added. "We have two options. One is to make it bigger, the other is to move out."
While the various extension plans are not shelved yet, organisers are now considering four possible new locations in the Paris suburbs, all over 15 kilometres away from the capital.
"We have four very serious projects," Ysern said. "It would be heartbreaking to leave Paris but we have to consider it."
A final decision on whether the tournament will remain in Paris is expected during a general assembly of the French Tennis Federation scheduled for February next year.
This year's French Open runs from May 24 to June 6.