French Open tournament director Amelie Mauresmo says it is hard to imagine the championships taking place without Rafael Nadal.
Nadal, a 14-time champion, has featured in every tournament since 2005 - but has not played since January's Australian Open because of a hip injury.
Nadal says he finds himself in a "difficult situation" and has already pulled out of next week's Madrid Open.
"It's obviously a possibility for him not to be able to be fit to come here to Roland Garros," Mauresmo said in an interview with BBC Sport on the Philippe Chatrier Court where Nadal beat Casper Ruud in last year's final.
"But the only thing I know for sure is that if there is one tournament he doesn't want to miss, it is this one. We are still five weeks away from the main draw. I am still hopeful, and I'll keep my fingers crossed.
"It will be hard [to imagine Roland Garros without him]. It would be hard if he doesn't come, to be honest.
"He's so much part of the history of the tournament for the last almost 20 years - it would be sad. But I am someone that is positive so I'm going to hope that things are going to get better for him."
Mauresmo was at Nadal's academy in Mallorca last month to present the 36-year-old with a replica of his statue, which was unveiled at Roland Garros two years ago.
The statue is three metres tall, and made entirely of steel. But Mauresmo says that will not ultimately be enough to commemorate Nadal's unprecedented run of success in Paris.
"We have this talk sometimes," she said.
"The opinions are very different with everyone - I think it would be hard to change the name of this [Philippe Chatrier] court, but, yes, we are having these conversations sometimes.
"We will need to do something to [celebrate] 14: maybe more one day. It is just something that is incredibly crazy, and in the history of sport quite unique."
Mauresmo also confirmed that, unlike at Wimbledon and other UK tournaments, Russian and Belarusian players will not need to sign a personal declaration of neutrality before being allowed to compete.
"No, I know it's the case in the UK. Here we are going to do the same as last year, so it's full neutrality - strict neutrality - so no flag, no anthem if one is winning, no name of the country announced by the speaker and of course no declaration of the player for the war."
She says that while the tournament and the French Tennis Federation have supported humanitarian relief in Ukraine, and hosted some of the country's players at the National Tennis Centre in Paris, there is not much more they can do during the fortnight.
"That's the tricky part of it," she said.
"We are a sport event and we decide to welcome everyone, so I believe we have to treat everyone the same way."
Mauresmo also believes the tournament has prepared the best it can for the possibility of disruption when the main draw gets under way on 28 May.
An environmental protestor caused a 15-minute delay to last year's men's semi-final between Ruud and Marin Cilic, and in recent months there have been widespread protests against President Macron's pension reforms
"We review our security measures very regularly - we are prepared in the best possible way, " she said, without wishing to expand.
"But definitely we know it's something coming up that is in the air, kind of, and we will see - we will face what is coming. There's no protest allowed in the grounds."
Mauresmo, who is in her second year as tournament director, also confirmed this year's night sessions will start half an hour earlier at the request of the players.
And there will be 16 players in each of the wheelchair singles draws, with one of the finals scheduled for the Philippe Chatrier Court.