Medvedev, the 2021 champion in New York, outclassed Nuno Borges, who was bidding to become the first Portuguese man to make a Grand Slam quarter-final, 6-0, 6-1, 6-3.
Top seed Sinner, who won his maiden Slam at the Australian Open this year, takes on Tommy Paul in the night session on Arthur Ashe Stadium.
French Open champion and women's world number one Iga Swiatek, meanwhile, hopes to take another step closer to a second US Open title when the 2022 winner faces Liudmila Samsonova of Russia.
Medvedev, the only former champion left after the defeats of four-time winner Djokovic and 2022 champion Alcaraz, is in the quarter-finals for the fifth time in six years.
The world number five easily downed 34th-ranked Borges whose challenge fizzled out under the weight of 51 unforced errors while Medvedev broke serve eight times.
"I played Tommy twice this season. I beat him once but I feel as if he should have beaten me both times," said Medvedev.
"I've had unbelievable battles with Jannik. It will be very physical for both of us."
Sinner, 23, faces Paul of the United States hoping to become the only man this year to reach the quarter-finals at all four Grand Slams.
The Italian made the last-eight at New York in 2022 where he squandered a match point in losing to eventual champion Alcaraz.
Paul, the 14th seed, is looking to join compatriots Frances Tiafoe and Taylor Fritz in the quarter-finals as the US looks for a first male Grand Slam champion since Andy Roddick triumphed in New York in 2003.
If Sinner gets through he will meet Medvedev for the fourth time this year.
Sinner came back from two sets to love down to defeat the mercurial Medvedev in the Australian Open final and came out on top in the Miami semi-finals.
Draper hails 'icon' Murray
Medvedev triumphed at Wimbledon in a five-set quarter-final.
Jack Draper became the first British man since Andy Murray in 2016 to reach the quarter-finals by seeing off Tomas Machac of the Czech Republic 6-3, 6-1, 6-2.
The 22-year-old left-hander has only dropped served once over four matches on his way to a maiden Slam quarter-final, winning 47 of 48 service games and saving 20 of 21 break points.
Draper hailed the influence of Murray, the former world number one and 2012 US Open champion, who retired from tennis following the Paris Olympics.
"He's a legend and an icon and if I have half the career that he had I will be a happy man," said the 25th seed who goes on to face either Alex de Minaur or Jordan Thompson who clash in an all-Australian battle later Monday.
Swiatek will play her 100th Grand Slam match when she meets 16th seed Samsonova who is chasing a first ever last-eight spot at the Slams.
Poland's Swiatek holds a 3-0 head-to-head edge over Samsonova but the 25-year-old Russian will be buoyed by making the quarter-finals of both WTA 1000 events in Toronto and Cincinnati on the eve of the US Open.
Should Swiatek prevail, she will take on US sixth seed Jessica Pegula who made the last-eight for the second time with a 6-4, 6-2 victory over Russia's Diana Shnaider.
Caroline Wozniacki, the runner-up to Serena Williams in 2014, faces Brazil's Beatriz Haddad Maia.
The winner of that clash will face 2023 semi-finalist Karolina Muchova who knocked out French Open and Wimbledon runner-up Jasmine Paolini, the fifth seed, 6-3, 6-3.
Muchova, ranked at 52, who only returned to the tour in June after 10 months out with a wrist injury, has yet to drop a set and knocked out two-time champion Naomi Osaka in the second round.
