NEW YORK — Defending champion Novak Djokovic and Carlos Alcaraz wound up on opposite sides of the US Open bracket in Thursday’s draw, meaning they could meet in another big final after Wimbledon and the Paris Olympics.

For that to happen, the No. 3-seeded Alcaraz might first have to get through a semifinal against No. 1 Jannik Sinner, whose doping case came to light this week. Sinner tested positive twice for an anabolic steroid in March but was cleared after it was determined the use was unintentional because the banned substance entered his system via a massage from his trainer.

Coco Gauff, who won her first Grand Slam title last year in New York, is seeded No. 3 and opens against Varvara Gracheva of France. Gauff and No. 2 seed Aryna Sabalenka could meet in the semifinals after playing for the trophy in the 2023 final. The winner could face No. 1 Iga Swiatek for the title.

The US Open starts Monday and ends Sept. 8.

Djokovic won his men’s-record 24th Grand Slam singles title last year in Flushing Meadows and has remained stuck on that total, losing to Sinner in the Australian Open semifinals, withdrawing from the French Open after injuring his right knee and losing to Alcaraz at the All England Club.

In a rematch at the Paris Games this month, Djokovic beat Alcaraz in a pair of tiebreakers for his first Olympic gold medal.

Djokovic, the No. 2 seed, hasn’t played since. Both he and Alcaraz will begin the US Open against players who emerge from this week’s qualifying tournament in New York.

Sinner, of Italy, plays American Mackenzie McDonald in the first round. Sinner, 23, won his first Grand Slam title at the Australian Open.

Two past US Open women’s champions who missed the tournament last year could face a tough time getting out of the first round in their return.

Naomi Osaka, who won two of her four major titles in Flushing Meadows and returned this season from maternity leave, opens against No. 10 seed Jelena Ostapenko, the 2017 French Open champion. Bianca Andreescu, the 2019 US Open champion who has dealt with a series of injuries since, was drawn to face No. 5 seed Jasmine Paolini, the runner-up this year at the French Open and Wimbledon.

Emma Raducanu, the 2021 US Open champion, opens against American Sofia Kenin, the 2020 Australian Open winner, in another first-round matchup of past major champions.

Men’s first-round matchups of note include No. 13 seed Ben Shelton, an American who reached the semifinals last year, facing 2020 US Open champion Dominic Thiem, who received a wild card into what will be his final Grand Slam tournament before retiring. No. 18 seed Lorenzo Musetti, who reached the Wimbledon semifinals and won an Olympic bronze medal for Italy, plays American Reilly Opelka.

Potential men’s quarterfinal matchups could be Sinner vs. 2021 US Open champion Daniil Medvedev, Djokovic vs. No. 6 Andrey Rublev, Alcaraz vs. No. 7 Hubert Hurkacz and 2020 runner-up Alexander Zverev vs. 2022 runner-up Casper Ruud.

The possible women’s quarterfinals are Swiatek vs. No. 6 Jessica Pegula, Sabalenka vs. Olympic gold medalist Zheng Qinwen, Gauff vs. two-time major champion Barbora Krejcikova and 2022 Wimbledon winner No. 4 Elena Rybakina vs. Paolini.