The last eight at the year's final Grand Slam will also feature a rematch of the 2014 final between former champion Marin Cilic and Kei Nishikori of Japan plus 2017 finalist Madison Keys against Spanish 30th seed Carla Suarez Navarro.
Serbian sixth seed Djokovic, who will cap the night session, is in familiar territory, appearing in his 11th quarter-final at Flushing Meadows, and looks like a favourite with five-times winner Roger Federer knocked out of his half of the draw.
The Wimbledon champion has appeared more impressive with each passing round and will be up against a confident Millman who is unseeded but flying high after stunning Swiss second seed Federer in the previous round.
Tsurenko, the only unseeded woman to reach this stage of the tournament, will be playing in her first Grand Slam quarter-final when she kicks off Wednesday's action on what is expected to be another steamy day in New York.
The Ukrainian upset Danish second seed Caroline Wozniacki in the second round and has been playing with a greater sense of focus and drive to suggest her work is far from done.
On the other side of the net will be 20-year-old Japanese Osaka, who won at Indian Wells this year and has used a lethal ground game and dogged determination to also reach her first Grand Slam quarter-final.
Seventh-seeded Croat Cilic, a three-times Grand Slam finalist who reached the showpiece game in Melbourne this year, has had a fairly easy path to the quarters apart from a five-set tussle in the third round with Australian Alex de Minaur.
Nishikori, who missed last year's U.S. Open with a wrist injury, has an 8-6 record against Cilic and the duo, who are two of the game's best battlers, are sure to slug it out again for the right to face either Djokovic or Millman.
Keys, who at 14 is the highest seed left in the women's draw, has shown a determination to go one step further than last year, having only dropped one set through her four matches.
But she will face a stern test from Suarez Navarro, who is brimming with confidence after arriving in New York on the heels of a finals appearance at New Haven.
Suarez Navarro upset former champion Maria Sharapova in the last round and needs another win to become the first Spanish women to reach the U.S. Open semi-finals since Conchita Martinez in 1996.
(Reporting by Frank Pingue; Editing by Ken Ferris)
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