Romania's Simona Halep continued to lead Women's Tennis Association (WTA) rankings released on Monday, ahead of Denmark's Caroline Wozniacki.
Williams can match Margaret Court's all-time record of 24 majors with another title at Flushing Meadows.
It was a second straight first-round exit at Flushing Meadows for Romania's Simona Halep, who dropped her opening match to Maria Sharapova last year.
Kiki Bertens defeated the world number one Simona Halep 2-6, 7-6 (8/6), 6-2 in the Cincinnati WTA final.
Roger Federer will be bidding to increase his tournament leading total, while Djokovic is keen to win the only Masters 1000 tournament missing from his trophy collection.
Rafael Nadal withdrew from next week's ATP Cincinnati Masters event as he prepares for the US Open.
In a gruelling 2hr 41min battle, French Open champion Halep prevailed 7-6 (8/6), 3-6, 6-4 over Stephens in a repeat of the duo's meeting in the final of Roland Garros earlier this year.
American third seed Stephens surged into Sunday's final against world number one Halep after overpowering Svitolina 6-3, 6-3 in the day's second semi-final.
The top-seeded Halep hammered 19 winners and won 77 percent of points on her first serve in the 88-minute contest.
Top seed Halep took no prisoners against Williams, blitzing the 38-year-old American 6-2, 6-2 in just 71 minutes to reach the quarter-finals.
Romania's Simona Halep continued to lead the Women's Tennis Association rankings released on Monday with 7,511 points, followed by Denmark's Caroline Wozniacki.
Serena Williams moved up one spot in the WTA rankings this week to world No.27.
Hsieh, the world number 48, battled back from 2-5 down in the final set and halted Halep who served for the match at 5-3 in the decider
Serena, 36, missed Wimbledon last year while preparing to give birth and has endured a rocky time since resuming her career earlier this year.
Simona Halep fought back from a set and a break down to finally claim her first Grand Slam title.
Simona Halep is still waiting for a maiden Grand Slam title after three previous final defeats, while Sloane Stephens is the reigning US Open champion.
Simona Halep will have an opportunity to finally lift a Grand Slam trophy when she faces US Open champion Sloane Stephens in her third French Open final on Saturday.
Simona Halep reached her third French Open final where she will face US Open winner Sloane Stephens for the title.