Holders Barcelona will visit Racing Santander, while Real Madrid travel to Albacete, in next week's Copa del Rey round of 16.
Atlético Madrid will play Deportivo La Coruña, and Athletic Club will face Cultural Leonesa, after Wednesday's draw in Las Rozas, Madrid.
The matches will be played between Tuesday and Thursday next week, with kickoff times to be confirmed shortly.
Barcelona, Madrid, Atlético and Athletic are currently in Jeddah, Saudi Arabia, competing in this season's Spanish Supercopa.
The other ties will see Burgos host Valencia, Real Betis play Elche, Real Sociedad play Osasuna and Alavés play Rayo Vallecano.
Barça beat Madrid 3-2 after extra time in last May's thrilling Copa del Rey final to complete a domestic treble.
The Catalan club have won the Copa del Rey a record 32 times, while Athletic have lifted the trophy 24 times, and Real Madrid have won it 20 times.
Athletic won the cup in 2024, ending a 40-year drought in the competition, while Madrid won it a year earlier.
In last month's round of 32, Barça beat Guadalajara 2-0, and Madrid needed a brace from Kylian Mbappé -- currently injured with a knee sprain -- to beat Talavera 3-2.
The Supercopa finalists -- with Barça playing Athletic and Real playing Atlético in semifinals on Wednesday and Thursday -- will play next week's Copa tie just days after returning from Saudi Arabia, with the Supercopa final to be played on Sunday night.
Complete draw:
Deportivo La Coruña-Atlético Madrid
Racing Santander-Barcelona
Cultural Leonesa-Athletic Club
Albacete-Real Madrid
Burgos-Valencia
Real Betis-Elche
Real Sociedad-Osasuna
Alavés-Rayo Vallecano