With three Masters tournaments and two Grand Slams in the space of seven weeks, players might have to make hard choices but French Open director Guy Forget is confident they will turn up at Roland Garros.
Djokovic will be nowhere near the centre court after losing his bid to overturn a second visa cancellation.
Osaka had pulled out of the French Open citing mental health and revealed that she suffered long bouts of depression since the US Open in 2018.
Czech fourth seed Tomas Berdych bulldozed his way into the second round of the French Open by thrashing Japanese qualifier Yoshihito Nishioka 6-0, 7-5, 6-3 on Monday.
It was only his second defeat in 11 years and 72 matches at Roland Garros, yet it came as little surprise for Rafael Nadal as the nine-time champion admitted he had his French Open quarter-final defeat to Novak Djokovic coming.
'I'm writing this to say I'm not going to do any press during Roland Garros,' Osaka tweeted
It took nearly five hours of gruelling tennis for Rafael Nadal to fend off Grigor Dimitrov and book a dream Australian Open final against Roger Federer but before Melbourne Park the Spaniard endured a season of heartache and doubt.
Australian Kyrgios was beaten in his first match in Lyon on Tuesday by Argentina's 94th-ranked Nicolas Kicker -- serving nine double faults during a 2-6, 6-4, 6-2 defeat.
Twice former champion Rafael Nadal will not play at this year's Wimbledon due to the wrist injury that forced the Spaniard out of the French Open, he said on Thursday.
Djokovic will need to win in Tokyo and then the US Open later this year to achieve the feat that has so far only been accomplished by Steffi Graf in 1988.
Fourteen-time Grand Slam champion Rafael Nadal on Wednesday pulled out of the Queen's club grass-court tournament, due to wrist injury.
Cecchinato in 'dreamland' after stunning David Goffin on Sunday
Australian controversial tennis star Nick Kyrgios has been slapped with the largest fine at the French Open for uttering an audible obscenity during his third round loss to Richard Gasquet.
The signs that things were going horribly wrong for Roger Federer were laid bare at Roland Garros.
Penpix of the top men's contenders at the 2017 French Open:
Yannick Noah is looking to restore old-fashioned values to the French Davis Cup team as he embarks on his third stint as captain.
Wimbledon officials on Tuesday said they are continuing plans for the grasscourt major to start on June 29 as scheduled even though French Open organisers postponed the claycourt Grand Slam to September due to the coronavirus pandemic.
Ash Barty ended Australia's 44-year wait for a home winner at the Australian Open when the world number one staved off a fightback from American Danielle Collins to complete a 6-3, 7-6(2) win.
Eighth seed Barty joins 1969, 1970 and 1973 champion Margaret Court and 1971 winner Evonne Goolagong-Cawley on the list of Australian women who have lifted the trophy here in the professional era.
Barty's athleticism is remarkable.
Up to 60% of usual capacity will be allowed to attend 2020 French Open, say organisers
A quick look at Rafael Nadal's domination of Roger Federer at Roland Garros.
Second seed Novak Djokovic tackles Croatia's Marin Cilic in the third round of the French Open on Friday as his attempt to win the only grand slam title to elude him gathers pace.
Man of many faces, Medvedev now a Grand Slam finalist
Cilic had never made it past the quarters in Paris but has now made the semis or better at all four majors.
Serena Williams overcame a gritty challenge from unseeded Dutchwoman Kiki Bertens, winning 7-6(7), 6-4, to reach the French Open final, in Paris, on Friday. She will meet Garbine Muguruza, who reached her second Grand Slam final when she beat Australia's Samantha Stosur 6-2, 6-4 in the first semi-final at Roland Garros.
Naomi Osaka is also the first woman to win a second Slam immediately after her first since Jennifer Capriati in 2001 but her meteoric rise has been followed by a distinct dip ahead of Roland Garros.
'But in mid-October, if we're able to come together and we've been able to provide revenue for 600 people, I think we will be very satisfied as a federation and I as a former player.'
Roger Federer's struggles continued when he was beaten 7-6 (2), 6-4 by fast-rising Austrian Dominic Thiem in the third round of the Italian Open in Rome, on Thursday.
The 12-time French Open champion unhappy with schedule.
'And for me to just be hitting a tennis ball in the United States right now and have people come and watch me play ... I would want to be myself in this situation rather than anyone else in the world.'
Maria Sharapova claimed her second French Open title when she floored Romanian fourth seed Simona Halep 6-4, 6-7(5), 6-4 after a marathon encounter in Saturday's final.
Images from the matches played on Day 8at the Roland Garros on Sunday
Japan's Osaka ended the stand-off with the French tennis federation (FFT) by withdrawing from the claycourt major
Sam Stosur powered into the French Open quarter-finals with a 7-6(0), 6-3 win against Simona Halep in Paris on Tuesday, adapting better to damp and heavy conditions than her higher-ranked Romanian opponent.
Federer had his first hit on Thursday at the ATP 500 event at the German city of Halle, where he has won 10 titles.
French Open organisers can't stop the rain from falling on Roland Garros, yet they could have done a better job at smoothing things out on Monday, according to Rafael Nadal and Novak Djokovic.
Two fellow Spaniards who have already beaten him on his favourite clay surface could lie in wait for favourite and defending champion Rafael Nadal at the French Open.
"But tomorrow is a new day and I have to move on. It's only the quarter-finals, and I want to fight for the title. That's what I came here for. I have to kind of direct my thoughts to the semis."
It will be the second time Nadal and Del Potro meet at Roland Garros. The previous match up saw the Spaniard beat Del Potro in straight sets in the opening round in 2007.
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