Novak Djokovic will begin his quest for a fourth US Open title against Damir Dzumhur.
The Serbian, who will be chasing an 18th grand slam singles triumph without Rafael Nadal and Roger Federer competing, could meet fourth seed Stefanos Tsitsipas or Alexander Zverev in the semi-finals.
Andy Murray, champion in 2012, faces Yoshihito Nishioka in the first round and could play 15th seed Felix Auger-Aliassime in round two.
Second seed Dominic Thiem is also in the bottom quarter of the draw. He begins against Jaume Munar and could meet Murray in round four.
Women's top seed Karolina Pliskova starts against Anhelina Kalinina and is on course for a fourth-round meeting with Angelique Kerber.
Fourth seed and 2018 champion Naomi Osaka begins against fellow Japanese player Misaki Doi and could face Coco Gauff in an exciting-looking third round.
Serena Williams, chasing grand slam singles title number 24, begins against compatriot Kristie Ahn. Her sister Venus has a tough first-round clash with 20th seed Karolina Muchova.
Second seed and Australian Open champion Sofia Kenin plays Yanina Wickmayer of Belgium in round one and could face Serena in the semi-finals.
Wild card Kim Clijsters is also in the bottom quarter of the draw and will start against 21st seed Ekaterina Alexandrova.
Play at Flushing Meadows begins on Monday.