Williams could face the second seeded Anett Konaviet of Estonia in the second round and the US Open finalist Leylah Fernandez of Canada in round four.
Should she advance, Williams could then face either the 12th seeded Coco Gauff of the USA or the 7th seeded Simona Halep of Romania in the semifinals.
Serena Williams could meet unseeded players Naomi Osaka of Japan, her sister Venus Williams of the USA or the 11th seeded Emma Raducanu of Great Britain or the top seeded Iga Swiatek of Poland in the final round match.
Like her sister in what could also be her final US Open match, Venus Williams will take on the unseeded Belgian Alison van Uytvanck in her open round match Tuesday as the second match scheduled on Arthur Ashe Stadium.
In 1997, Venus Williams reached the US Open final in her tournament debut before twice winning the title.
In the bottom half of the men's draw, Nadal could face the third seeded Carlos Alcaraz of Spain in the semifinals.
In the top half of the men's draw, American hopefuls Tommy Paul, seeded 29th and the 10th seeded Taylor Fritz could meet in round four.
The 23rd seed and Wimbledon finalist Nick Kyrgios of Australia could meet the current world number one and defending US Open champion Daniil Medvedev also in round four.
Nadal could only face Medvedev or Kyrgios in the final.
Missing from the US Open draw is the Wimbledon champion and former world number one Novak Djokovic of Serbia who has not been able to enter North America due to being unvaccinated against Covid-19.