ROME, Italy - World No.1 Naomi Osaka made it clear she is eyeing the No.1 seed at Roland Garros, but to reach that milestone she would once again have to hold off No.2 and reigning French Open champion Simona Halep this week at the Internazionali BNL d'Italia.

Halep bowed out in the second round of Rome in a three-set thriller against 19-year-old Czech talent Marketa Vondrousova, 2-6, 7-5, 6-3 on Thursday, allowing Osaka to secure the No.1 ranking after Rome and sit as the provisional No.1 seed at Roland Garros.

Official Roland Garros seedings will be released on Monday, May 20th, and are based on the WTA rankings released that day. Halep was the only player at the start of the tournament who had a chance to overtake Osaka, but the Romanian needed to win the tournament with Osaka losing before the quarterfinals. 

While three players began last week's Mutua Madrid Open with a shot at overtaking Osaka, the 21-year-old's strong clay season has whittled that number down to just one. Halep had a chance to retake the No.1 ranking in Madrid but fell short to Kiki Bertens in the final. 

"I just feel like it's the way, not necessarily how you perceive yourself, but how other people perceive you, even outside of tennis," Osaka told reporters at All Access Hour ahead of Rome. "Like people are talking or whatever, and then they would be talking about you. I feel like there's a big difference between saying No. 1 in the world versus No. 2.

"I think it's little stuff like that. And for me, after the Australian Open they said that I was going to be No. 1. But for me, I feel like the biggest impact would be being seeded No. 1 in a Grand Slam. That was always something that was on my mind.

"Of course, I've been telling people I don't really care about rankings as long as I can get into a tournament. I feel like that is true.

"At the same time, everyone knows this about me: the Grand Slams are the things that I care about the most. 

"It's always been a dream for me [to be top seed at a Slam]. Hopefully I'm able to do that."

In the midst of her best clay season ever, Osaka comes into Rome having made the semifinals in Stuttgart and the quarterfinals in Madrid, where she served for the match but fell short against Belinda Bencic 7-5 in the third set. Osaka had just 200 points to defend during the clay swing and she's already tallied 400 points through her first two events. She has never advanced past the third round in Rome. 

Halep came into Rome with a 7-1 record on clay this year, having made the final in Madrid. She had made the final of Rome the last two years, but had yet to win the title. 

Speaking after her loss in Rome, Halep cut a relaxed figure when asked about returning to Paris, where she cemented her place at the top of the game by winning her maiden major last year. 

"Well, I can't expect anything because to be a defending champion in Grand Slam is for the first time for me, so it's something new," Halep said. "I will be more relaxed. I will try to enjoy more. Hopefully I can win some matches.

"I don't know what is going to happen in French Open. I always said in the last few months that tennis is very open now. The top is open. Anyone can win.

"Kiki Bertens has a chance, in my opinion. Stephens again. Many players are playing well on clay. We will see. I'm very curious, as well."

This post has been updated to reflect Simona Halep's second round loss.