Holders Barcelona were drawn against city rivals Espanyol in the Copa del Rey last 16 on Friday.
In other derby clashes Atletico Madrid take on Rayo Vallecano and Sevilla come up against Real Betis.
Real Madrid were the big names missing from the draw, Rafael Benitez's side kicked out for fielding an ineligible player against third-tier Cadiz, who will play La Liga outfit Celta Vigo.
The first-leg matches will be played on January 6-7 with the return fixtures set for January 12-13.
Copa del Rey last 16 fixtures:
Barcelona v Espanyol, Valencia v Grenada, Mirandés v Deportivo La Coruna, Cadiz v Celta Vigo, Real Betis v Sevilla, Athletic Bilbao v Villarreal, Eibar v Las Palmas, Rayo Vallecano v Atletico Madrid