The Serb, 37, who is tied with Margaret Court on 24 major singles titles, plays the 28th seed in the evening session at 00:00 BST on Arthur Ashe Stadium.
Defending champion Djokovic and Popyrin are meeting for the third time at Grand Slams this year, with the Serb winning in four sets at the Australian Open and Wimbledon.
“I’m happy to win four sets another time. Don’t get me wrong. But he keeps on getting closer and closer, knocking on that door,” said Djokovic.
“He’s been playing some great tennis, so no reason for him not to believe that he can put up a great performance, and he’s going to go for the win. I know that.
“But I know what to expect as well, I’m going to do my homework and see what needs to be done.”
Djokovic reached the third round after compatriot Laslo Djere retired hurt in their second-round tie, while Popyrin, 25, beat Spain’s Pedro Martinez in straight sets.
The Serb is a four-time winner at Flushing Meadows while Popyrin has not made it past the third round on the two previous occasions he’s reached it.
In the women’s draw, American third seed Coco Gauff continues the defence of her title against Ukraine’s Elina Svitolina on Arthur Ashe Court from 17:00 BST.
Gauff, 20, beat Germany’s Tatjana Maria in straight sets to set up the meeting with 27th seed Svitolina, who breezed past compatriot Anhelina Kalinina 6-1 6-2.
Gauff’s triumph was her ninth straight victory at the US Open but faces a player in good form in former world number three Svitolina, who did not drop serve once in victory against Kalinina.
The tie marks the fifth meeting between the pair, with two wins apiece.
Last on Arthur Ashe Court Belarusian second seed Aryna Sabalenka takes on Russian 29th seed Ekaterina Alexandrova.
Two-time Australian Open champion Sabalenka will be hoping she can go one better after finishing as runner-up in New York last year, while Alexandrova is aiming to reach the fourth round at Flushing Meadows for the first time.
Who else is in action on day five?
Closing the day session on Arthur Ashe Court is an all-American tie between men’s 13th seed Ben Shelton and 20th seed Frances Tiafoe.
The mouth-watering contest is a rematch of their quarter-final in New York last year, which Shelton won in four sets.
Unseeded Shelton, who at 21 is five years younger than friend and mentor Tiafoe, was the underdog on that occasion but goes into Friday’s tie as the favourite.
“I think everything that comes in your career, all the highs and lows, only sets you up for better moments ahead,” said Tiafoe.
“I’m super excited for the match, and any opportunity to do it again.”
Other third-round ties see German fourth seed Alexander Zverev face Argentina’s Tomas Martin Etcheverry and Russian sixth seed Andrey Rublev, who is a four-time quarter-finalist at Flushing Meadows, take on Czech 32nd seed Jiri Lehecka.
On the women’s side of the draw Chinese seventh seed Qinwen Zheng plays Germany’s Jule Niemeier and American 14th seed Madison Keys competes against Belgian 33rd seed Elise Mertens.
