Los Che overcame third-tier side Atletico Baleares in the last round thanks to Marcos Andre's goal in the opening minute of the game.
Cadiz, meanwhile, have reached the last-eight for the first time since the 2005-06 season after beating Sporting Gijon 4-2 on penalties in the round of 16.
The Yellow Submarine are hoping to put their La Liga troubles behind them by advancing further into the competition, with the side battling relegation in 18th place on the league table.
Valencia vs Cadiz Head-To-Head
The Bats have won three of their last seven clashes with Cadiz, losing just once.
However, their last encounter, coming in October last year, ended in a goalless stalemate.
Valencia Form Guide (all competitions): W-L-W-D-L
Cadiz Form Guide (all competitions): W-L-W-D-W
Valencia vs Cadiz Team News
Gabriel Paulista and Jasper Cillessen will miss out for the Bats through injuries.
But on the bright side, Maxi Gomez and Daniel Wass are available for selection after sitting out with COVID-19.
Jose Gaya also returns from a one-game ban for the red card he received against Sevilla in La Liga.
Injured: Gabriel Paulista, Jasper Cillessen
The Yellow Submarine won't have Jose Mari and Alberto Perea available as they're currently in the treatment room, while Fali is ruled out until mid-February.
Alvaro Jimenez joined Ibiza on loan for the remainder of the campaign while Jon Ander Garrido left for Mirandes.
Injured: Jose Mari, Alberto Perea, Fali
Unavailable: Alvaro Jimenez, Jon Ander Garrido
Valencia vs Cadiz Predicted XI
Valencia (4-4-2): Jaume Domenech; Thierry Correia, Mouctar Diakhaby, Omar Alderete, Jose Gaya; Dimitri Foulquier, Daniel Wass, Hugo Guillamon, Yunus Musah; Maxi Gomez, Goncalo Guedes.
Cadiz (4-4-2): Jeremias Ledesma; Isaac Carcelen, Varazdat Haroyan, Victor Chust, Pacha Espino; Salvi, Alex Fernandez, Fede Emeterio, Ivan Alejo; Alvaro Negredo, Ruben Sobrino.
Valencia vs Cadiz Prediction
Cadiz have reached the furthest in the competition since 2006 but they've frankly had an easy run so far against sides residing in lower divisions.
The Bats are a totally different kettle of fish, and have an envious attacking arsenal that can take them apart. We expect Valencia to secure a narrow victory.
Prediction: Valencia 2-1 Cadiz