(CNN)Serena Williams has won virtually everything on offer in women's tennis, so it's no surprise she's feeling relaxed -- in a dream world, even -- about the prospect of setting another piece of sporting history.
French Open 2015: Serena Williams 'living a dream'
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The world No. 1 is aiming to win the 20th grand slam singles title of her illustrious career at the French Open, which would put the American third on the all-time list behind only Steffi Graf (22) and Margaret Court (24).
She crashed out in the second round last year as defending champion, but the 33-year-old believes she is ready for more success at Roland Garros despite an elbow injury that caused her to withdraw from this month's event in Rome.
"The elbow is much, much better," Williams told reporters in her pre-tournament press conference.
"I was worried about it, but lately I have been getting some really good treatment that has been able to alleviate it and make the symptoms go down substantially.
"So I feel a lot better going forward in the tournament and just getting through it. The good thing is that every day, it's getting better. I'm just starting to serve harder, so I'm like, 'Yes.'"
Williams is level on 19 singles titles with fellow American Helen Wills Moody, who won 31 grand slams in all formats during the 1920s and '30s. Williams has 34 overall, with 15 in women's and mixed doubles.
"I feel like there is still plenty of time. Honestly, if I get to 20, that would be great," she said.
"If I get past that, that would be great. I think 19 is pretty awesome, too. I never thought I would be at 19. I never thought I would make it this far.
"Every day I feel like I'm living a dream. I don't want to wake up because it's been really good."
Williams is in the same half of the draw as former world No. 1 Victoria Azarenka, who she could face in the last 32 -- and if she wins that there could be a fourth-round clash with her older sister Venus.
Williams will begin against 191st-ranked Czech Andrea Hlavackova, who came through qualifying.
Young Spaniard Garbine Muguruza, who thrashed Williams in straight sets in Paris last year, features in Sunday's opening matches of the tournament. The 21st seed will play 155th-ranked Croatian Petra Martic
Muguruza is in the same half of the draw as second-ranked defending champion Maria Sharapova, who will play Kaia Kanepi in her opening match.
The Russian faces a possible semifinal clash with world No. 3 Simona Halep, who she beat in last year's title match.
The Romanian is also in action on Sunday, playing 91st-ranked Russian Evgeniya Rodina, while 2008 champion Ana Ivanovic takes on Kazakhstan's Yaroslava Shvedova.
In the men's draw, second seed Roger Federer opens his bid for a record-extending 18th grand slam title -- and second in Paris -- against Colombian qualifier Alejandro Falla on Sunday.
Japanese fifth seed Kei Nishikori and Swiss No. 8 Stanislas Wawrinka are also playing Sunday.
Defending champion Rafael Nadal and world No. 1 Novak Djokovic could meet as early as the quarterfinals, with the Spaniard ranked seventh as he seeks an unprecedented 10th title in his favorite clay event.
The winner of that match could face third seed Andy Murray in the semis -- both the Scot and Djokovic are seeking their first French Open success.