Fourth-seeded Casper Ruud advanced here on Wednesday with a 7-5, 7-6(1) win over Dutchman Botic van de Zandschulp in the second round of the Monte-Carlo Masters, the first clay-court Masters' event of the season.
The 31-year-old Fognini will take on Serbia's Dusan Lajovic, another debutant in a Masters 1000 final, who defeated Daniil Medvedev of Russia 7-5, 6-1 in a little more than 90 minutes in Saturday's other semifinal.
World No.3 Cilic needed one hour and 33 minutes to knock out Verdasco, World No. 37, on Wednesday night.
If former World No. 1 Djokovic wins his upcoming match, he may face current World No. 1 Rafael Nadal in the quarter-finals.
Nishikori, aged 28, is set to play against Russia's Daniil Medvedev, World No.49, in the next round.
Nadal rose in the rankings after winning 6-1, 6-3 over his compatriot Albert Ramos-Vinolas.
The Indo-Uruguayan pair will now contest Poland's Romain Arneodo and France's Hugo Nys.
Murray, the world's No.1, defeated No. 32 Muller 7-5, 7-5 in one hour and 55 minutes.
Mannarino advanced to the third round of the tournament after stunning Tsonga.
