Williams, the 23-time Grand Slam title winner who has hinted she will make the event her farewell tournament, is in the same quarter of the draw as second seed Anett Kontaveit of Estonia.
The 40-year-old American superstar, whose first Grand Slam title came at the 1999 US Open, would meet Kontaveit in the second round if both win their opening matches at the year's final Grand Slam event, which begins Monday.
Williams, who is one title shy of the all-time record 24 Slam crowns won by Margaret Court, could have quite a path to the final were she to make a shock run on the Flushing Meadows hardcourts.
She could face Canada's 14th-seeded Leylah Fernandez, a 19-year-old who was last year's US Open runner-up, in the fourth round and Tunisia's Ons Jabeur, this year's Wimbledon runner-up, in the quarter-finals.
The winner from Kontaveit's quarter of the draw could meet Greek third seed Maria Sakkari or Romania's seventh-seeded Simona Halep in the semi-finals.
The other half of the bracket features top seed Iga Swiatek of Poland, this year's French Open champion, and Spanish fourth seed Paula Badosa.
Swiatek could meet US eighth seed Jessica Pegula in a quarter-final while Badosa could face sixth seed Aryna Sabalenka.
Japan's Naomi Osaka, a four-time Grand Slam champion, is also in Badosa's quarter of the draw.
She would meet defending champion Emma Raducanu, the 11th seed from Britain, in a third-round showdown and Sabalenka in the round of 16.
Victoria Azarenka, a two-time Australian Open winner, could meet Badosa in the third round.
Venus Williams, a seven-time Grand Slam champion, could meet Sabalenka in the third round, meaning she could only face younger sister Serena in a US Open final, likely meaning the siblings have faced each other for the final time in a major singles draw.
Serena indicated in interviews earlier this month that she is ready to move on with other areas of her life, including possibly having a second child.
Medvedev to face Kozlov
The men's draw opened slightly with Wimbledon champion Novak Djokovic, a 21-time Slam singles winner, pulling out just before the draw because he cannot enter the United States while unvaccinated for Covid-19.
Top-ranked defending champion Daniil Medvedev will face American Stefan Kozlov in his first match next week while second seed Rafael Nadal starts against Australian Rinky Hijikata.
Nadal, a men's record 22-time Grand Slam champion seeking his fifth US Open title, could face Britain's Cameron Norrie in the quarter-finals and countryman Carlos Alcaraz, the third seed, in the semi-finals.
Defending champion Medvedev could meet Greek fourth seed Stefanos Tsitsipas in the semi-finals and Canadian sixth seed Felix Auger-Aliassime in the quarter-finals.
Alcaraz has Polish eighth seed Hubert Hurkacz in his quarter of the draw while Norway's fifth-seeded Casper Ruud is in Tsitsipas's quarter.
Britain's Andy Murray, a three-time Grand Slam winner, is in the Tsitsipas quarter of the draw. Murray opens against Argentine 27th seed Francisco Cerundolo and could meet Italian 15th seed Matteo Berrettini in the third round and Tsitsipas in the round of 16.
Swiss Stan Wawrinka, a three-time Grand Slam winner, opens against a qualifier and could meet Ruud in the round of 16.
Australian Nick Kyrgios, the 23rd seed, opens against compatriot and doubles partner Thanasi Kokkinakis with Spanish 16th seed Roberto Bautista Agut a possible third-round foe and Medvedev potentially facing him in the round of 16.
