Top seed Sinner, whose doping case has dominated the lead-up to the US Open, faces a tough road to the New York final while in-form Aryna Sabalenka will also be tested, according to the draw released on Thursday.
Sinner won in Cincinnati this week to claim his fifth title of a breakout season before the revelation that he avoided a ban over two positive tests in March as it was ruled the Italian bore no fault or negligence for the violations.
The Australian Open champion is projected to face 14th seed Tommy Paul in the fourth round, 2021 winner Medvedev in the quarter-finals, Alcaraz in the semis and defending champion Djokovic in the final.
Djokovic, who has not competed since winning the gold medal at the Paris Olympics, will begin against a qualifier and is expected to meet Andrey Rublev in the quarter-finals and fourth seed Alexander Zverev in the semis.
Reigning French Open and Wimbledon champion Alcaraz will also start against a qualifier and could face Poland's Hubert Hurkacz in the quarter-finals.
In the women's draw, top seed Iga Swiatek, a five-time Grand Slam winner who reached the fourth round last year, will start against a qualifier and faces a potential quarter-final clash against Canadian Open champion and Cincinnati runner-up Jessica Pegula.
Second seed Sabalenka, looking to go one further after finishing runner-up in New York last year, returns well-rested after a mid-year break to focus on her health. She will be confident about her chances after winning the tune-up event in Cincinnati.
Sabalenka's fortnight may include a third-round date with Ekaterina Alexandrova followed by a fourth-round clash with Madison Keys, Zheng Qinwen in the quarters, defending champion Coco Gauff in the semis and Swiatek in the final.
Gauff, who last year became the first American to win a US Open singles title since 2017, will begin her title defence against Frenchwoman Varvara Gracheva.