Ruud, who reached the final of the French Open earlier this year, recorded a hard-fought victory over Jaume Munar in the quarter-final on Friday.
The Austrian has beaten the likes of Varillas, Hugo Gaston and Federico Delbonis but Berrettini is undoubtedly his biggest challenge so far.
Albert Ramos-Vinolas beat home favourite Dominic Stephan Stricker in the round of 16 by a score of 6-3, 4-6, 6-1.
Casper Ruud beat Jiri Lehecka 6-3, 6-4 in the round of 16 to make it through to the quarter-final.
In Gstaad, the Italian beat Richard Gasquet in the round of 16 by a score of 6-4, 6-4 to make it through to the quarter-final.
Dominic Thiem beat Federico Delbonis in the second round of the Swiss Open to advance to the quarter-final.
Albert Ramos Vinolas v Dominic Stricker will take on each other on Thursday, July 21 in the second round of the 2022 Swiss open Gstaad.
Pedro Martinez v Elias Ymer will take on each other on Thursday, July 21 in the second round of the 2022 Swiss open Gstaad.
Nicolas Jarry vs. Yannick Hanfmann will take on each other on Thursday, July 21 in the second round of the 2022 Swiss open Gstaad.
Matteo Berrettini vs Richard Gasquet will take on each other on Thursday, July 21 in the second round of the 2022 Swiss open Gstaad.