The 12th seed has bitter memories of New York, where he squandered a two-set head start in the final to Austrian Dominic Thiem three years ago.
Also a semi-finalist in 2021, he has flown under the radar this year as fans focus their attention on a potential final between burgeoning rivals Djokovic and Alcaraz.
"It's natural for the media to find rivalries," he told reporters.
"Novak said it very well, there are other players that can play in the draw, there are other players that both of those guys have lost to."
Zverev will begin the Saturday evening programme on Louis Armstrong Stadium against Bulgarian Grigor Dimitrov, whom he has beaten twice this year already - including on the hard court at Cincinnati last month.
Many New Yorkers ditched their Labor Day weekend barbecues as they headed for the hard courts of Queens, piling into the Billie Jean King National Tennis Center under hot and sunny conditions to see who will advance into the last 16.
Ons Jabeur has come within one victory of hoisting a Grand Slam trophy on multiple occasions, as she reached the last two Wimbledon finals and was also runner-up to world number one Iga Swiatek at Flushing Meadows 12 months ago.
Battling a bout of flu, she will be hoping she can still produce her best tennis when she kicks off the evening session on Arthur Ashe Stadium against Czech 31st seed Marie Bouzkova.
"Another test," Jabeur told reporters when asked about the match-up after surviving tough battles in the first two rounds.
"It's going to be tough playing her, but I'm going to get ready and hopefully prepare well for the match."
Russian Daniil Medvedev will close out the action on Ashe against little-known third-round opponent, Sebastian Baez of Argentina.
The third seed, who lifted the trophy two years ago, dropped a set against Australian Christopher O'Connell in the second round in an early scare.
Czech Wimbledon champion Marketa Vondrousova meanwhile rounds out the action on Armstrong against Russian Ekaterina Alexandrova, whom she beat on the hard court in Adelaide this year.
