Gauff arrived in New York in red-hot form after titles in Washington and Cincinnati and has been heavily backed by home fans in her bid to become the first U.S. woman to capture a Grand Slam title since Sofia Kenin in 2020.
The 19-year-old has wobbled in two of her opening three matches, however, and could face a tricky test on Arthur Ashe Stadium with veteran Wozniacki enjoying a dream run in her first major after more than three years out of the sport.
"I never thought I would ever be in this position, especially after she retired and came back. She's still a really fit player," Gauff said of the 33-year-old former world number one before their fourth-round match.
"It's not going to be an easy match. She probably knows my game pretty well. I know she's watched tennis when she was retired.
"I know a little bit of her just from watching her growing up. It's going to be really cool. I'm excited. Playing a legend like her is really exciting."
Soaring temperatures are expected to make life difficult for players over the next few days with a heat wave set to hit New York but Djokovic will welcome competing at night again after a draining five-setter against Laslo Djere.
The 36-year-old will meet Croatian qualifier Borna Gojo, seeking a victory that will take him a step closer to a men's record-extending 24th major title.
Defending champion Swiatek takes on 20th seed Jelena Ostapenko who is looking to become the first player to defeat the Pole four times.
"With Jelena, it's a bit like one day she can play a perfect match and put everything in even though she's really risking and the other day can be different," Swiatek said.
"You never know what to expect. But I kind of accept that all these players they're going to play the best tennis against me."
Tommy Paul and Ben Shelton kick off the day's action on Ashe in an all-American clash while compatriot Frances Tiafoe faces Australian Rinky Hijikata on Louis Armstrong Stadium.
Taylor Fritz will also be in action on the second showcourt against Swiss Dominic Stricker. It is the first time since 2011 that four American men have reached the US Open fourth round.
"It's this progression we've had for a while," Fritz said.
"Someone achieves something big, then someone else comes and wants to match him or one-up him and it's the cycle that keeps going. We're all such good friends, it's motivating."