Second seed Federer takes on Australia's John Millman on Arthur Ashe Stadium. He is the big favourite to progress and set up a potential quarter-final against Novak Djokovic.
Sharapova won the title back in 2006 and remains on target in New York. The Russian faces Spain's Carla Suarez Navarro who knocked out sixth seed Caroline Garcia in the third round.
The action kicks off on Arthur Ashe Stadium at 7 p.m. ET (midnight BST) with Suarez Navarro against Sharapova. They are followed by Federer's meeting with Millman.
In the United States live coverage is available on ESPN. Amazon Prime has exclusive coverage in the United Kingdom. A complete television schedule is available from the tournament's official website.
Federer faces Australian opposition for the second match in a row after defeating Nick Kyrgios in straight sets in the third round.
The Swiss star was at his imperious best to brush aside the challenge of the 23-year-old. He will be expected to do the same to the unseeded Millman.
The two players have only ever met once before. Federer won in three sets on hard courts at the 2015 Brisbane International in Australia.
Federer is yet to drop a set at this year's tournament. He opened with a routine win over Japan's Yoshihito Nishioka and followed that up with a comfortable victory over Belgium's Benoit Paire.
Millman is entering new territory at a Grand Slam. The 29-year-old is into the second week of a major for the first time in his career.
The Australian has endured numerous setbacks. Ahead of the match he has spoken about the injuries he has suffered, per AAP (h/t ESPN).
"I've had three surgeries in my career, two shoulders and the last one a groin, and every time I've had extreme doubts if would get back," he said. "But I have a great team around me that pick me up when I feel sorry for myself. Without them, I wouldn't have this opportunity."
Millman knocked out Russia's Mikhail Kukushkin in the third round after earlier wins over 14th seed Fabio Fognini and Jenson Brooksby.
Facing Federer on Arthur Ashe Stadium in the fourth round of the U.S. Open is reward for all his hard work. However, it would be a massive shock if he were to go any further in the tournament.
Sharapova's hopes of winning a fifth Grand Slam title are increasing. The 22nd seed has not dropped a set yet in wins over Patty Schnyder, Sorana Cirstea and 10th seed Jelena Ostapenko.
She also has a formidable record under the lights at Flushing Meadows, per Stuart Fraser at The Times:
Sharapova has a strong record against Suarez Navarro too. She has won four of the five meetings between the two players.
The Spaniard is into the fourth round at the U.S. Open for the third year in a row. However, she has been taken to three sets in every round of this year's tournament.
Sharapova appears to have the edge ahead of their clash in the fourth round in New York. The winner of the match will go on to face 14th seed Madison Keys.