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.
Garcia defeated Elisabetta Cocciaretto in the round of 16 by a score of 0-6, 6-3, 6-4 on to advance to this stage of the competition.
Irina-Camellia Begu and Diane Parry will take on each other on Friday, July 22 in the quarter-final of the 2022 WTA Palermo open.
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.
In the quarterfinal of the 2022 WTA Hamburg open on Thursday, fourth seed Aliaksandra Sasnovich will face seventh seed Maryna Zanevska.
Federer has expressed his intention to first play at the Laver Cup alongside Rafael Nadal in London later this year. And he has pencilled in an appearance at the Swiss Indoors tour...
Aslan Karatsev will take on Hugo Gaston in the round of 16 of the 2022 Nordea Open.