Alcaraz was in mixed doubles action with Serena Williams this week and has now ended up in a stacked half of the draw alongside Djokovic.
If he can get past his Russian opponent, Alexander Bublik could await in the fourth round. He then may face Cincinnati winner Arthur Fils - who is up against former world number three Stefanos Tsitsipas in the first round - or Canadian Open victor Ben Shelton in the quarter-finals.
Djokovic opens up against Mariano Navone, before a potential blockbuster second-round matchup with either Stanislas Wawrinka - who is playing at his final Grand Slam - or Matteo Berrettini. The in-form duo of Brandon Nakashima and Frances Tiafoe could be last-16 and quarter-final opponents, respectively.
In the other half, top seed Alexander Zverev faces a potentially tricky encounter against Lorenzo Sonego first up, with either Rafa Jodar or Alex de Minaur likely quarter-final opponents.
Meanwhile, third seed Felix Auger-Aliassime takes on Rinky Hijikata, but he could go head-to-head with unseeded Karen Khachanov in the second round. Learner Tien is a potential fourth-round rival, while Taylor Fritz or Flavio Cobolli are in the same quarter.
On the women's side of the tournament, Rybakina and Swiatek are on a collision course in the last eight, after they met in both WTA 1000 events ahead of the US Open. Swiatek came out on top in the Toronto final, before Rybakina retired in their Cincinnati meeting. The Kazakh's health status is still unclear.
Rybakina opens against wildcard Thea Frodin, while Naomi Osaka is also a potential heavyweight fourth-round opponent.
Alongside Rybakina, Coco Gauff and Jessica Pegula also have a chance to claim the world number one ranking at the US Open, but they will have to win the tournament to have a chance.
Fourth seed and Cincinnati champion Gauff is in Rybakina's half, and opens against Turk Zeynep Sonmez. Young stars Iva Jovic or Alexandra Eala may be her fourth-round opponent, and Mirra Andreeva or Amanda Anisimova potential quarter-final opponents.
In the top half, world number one Aryna Sabalenka faces an extremely challenging run. Her first opponent is Camila Osorio, with two-time Grand Slam champion Barbora Krejcikova awaiting in round three and Diana Shnaider - who beat her at Roland Garros - in the fourth round. Marta Kostyuk and Linda Noskova are also in her quarter.
Finally, third seed Pegula begins her quest for a maiden Grand Slam against Elena-Gabriela Ruse, while seven-time major champion Venus Williams could be a second-round opponent - if she can end her 14-match losing run against Sofia Kenin.
Her quarter-final opponents could be either Elina Svitolina or Karolina Muchova.