The two-time defending women's champion is projected to face Serbian eighth seed Ana Ivanovic in the quarterfinals. Although Williams leads their career head-to-head 7-1, former world number one Ivanovic ousted the American in the fourth round of the Australian Open in January.
Williams could find herself up against another player who has managed to get the better of her on a major stage in the round of 16, Australian Samantha Stosur, Sport24 reported. Stosur, seeded 24th, stunned Williams in the 2011 US Open final.
In the semi-finals, Williams could find herself facing third-seeded Petra Kvitova or seventh-seeded Eugenie Bouchard. Kvitova and Bouchard were put on course for a quarterfinal clash that would be a re-match of the Wimbledon final in which Czech Republic's Kvitova routed the rising Canadian star to claim a second Wimbledon title.
Williams, attending the draw ceremony on Thursday, said that she wouldn't be looking that far ahead in the draw.
Having failed to make it out of the fourth round at any Grand Slam this year, the 17-time major winner won't be taking anything for granted, even against unheralded first-round opponent Taylor Townsend.
Williams, who despite her lack of Grand Slam success this year has looked strong in taking two hardcourt titles in three weeks in preparation for the Open, said that the way her year's been going, she is worried about every single match.
She said that she feels like she is playing well, she has a chance to win her match, like she has the match on her racquet. But, Williams added that anyone could surprise her.
Williams' elder sister Venus landed in the bottom quarter of the draw headlined by world number two and second seed Simona Halep and fifth-seeded Russian star Maria Sharapova.
Sharapova will open against fellow Russian Maria Kirilenko, while Halep will face US wildcard Danielle Rose Collins. Meanwhile, Venus, a seven-time Grand Slam champion, would feel like a youngster, as she would be opening against 43-year-old Japanese veteran Kimiko Date-Krumm, the report added.