National tennis federation delegates could vote on Sunday to move the French Open from Roland Garros out to the suburbs of Paris from 2016.
Venues in Versailles, Gonesse and one close to Disneyland Paris are vying with the existing site to host the annual clay court event as costs, space and the need for technological advances become paramount.
Roland Garros will renovate and extend its ageing and restricted site if it gets the nod to continue although there has been media speculation that a final decision might not be reached by the French Tennis Federation's general assembly on Sunday.
Reports have said the existing site of the only clay grand slam and Versailles will both be chosen as preferred bidders with a run-off between the two taking up to three months.
Leading women's player Kim Clijsters told Reuters earlier this week she was torn over the issue.
"For me, to move away from Roland Garros, it takes my childhood away a bit," the Belgian said.
"But the way architecture and technology have gone in the last 20-30 years, it's only going to be better for the sport if you can have stadiums with roofs and better facilities for players and fans."
France's retired former world number one Amelie Mauresmo has made up her mind, however.
"It's been years now that I thought it was necessary to move the tournament," she said. "Even if there is a way of keeping it in Paris, I've got the impression that in 10 years the question will be asked again." (Additional reporting by Chrystel Boulet-Euchin and Eric Salliot)