Alaves defeated Alcorcon to advance and will believe they can make it to the final if they restrict the hosts in the opening game.
Barcelona and Atletico Madrid meet in the other semi-final to decide which Spanish giant advances all the way to the end of the competition.
Here is how you can watch the first instalment of the last-four fixture:
Date: Thursday, Feb. 2
Time: 8 p.m. GMT/3 p.m. ET
TV: beIN Sports USA (U.S.)
Real Madrid's cup ambitions were dashed by a valiant Celta side in the quarter-finals, defeating the champions of Europe 4-3 on aggregate.
Los Blancos had been expected to travel to the Balaidos Stadium and prevail after losing the first leg, but Cristiano Ronaldo and his team-mates could not overturn the disadvantage.
The Sky Blues will be delighted the draw fell in their favour, as Barca and Atletico meet in the other semi-final.
Celta are enjoying a fine campaign, residing in eighth in La Liga and just outside the UEFA Europa League positions.
However, Alaves are also fighting the good battle in Spain's top division and lie 12th. They are 11 points clear of the relegation zone, allowing success in the Copa to become a focus and priority.
Fans of Spanish football might be underwhelmed by a cup match involving mid-table sides, but the prospect of getting to the final is equally realistic for both clubs.
Celta have announced the signing of Danish attacking midfielder Andrew Hjulsager, per their official website (h/t Adriana Garcia of ESPN FC).
The player has impressed in the Danish Superliga, scoring seven goals in 19 appearances for Brondby, per Garcia.
The transfer will give Celta coach Eduardo Berizzo flexibility in attack with Chile winger Fabian Orellana going to Valencia on loan, per club statements (h/t Garcia). Berizzo had already banished Orellana for "an unacceptable lack of respect," per EFE (h/t Padraig Whelan of Marca).
Previous to the loan move, Celta sporting director Felipe Minambres confirmed the player would not feature for the team again, per EFE (h/t Whelan).
Based on the coach's report, the club has decided to look for a fresh start for Orellana in January.
We will attempt to find the best solution, which would be a sale.
The club comes first, above all individuals and we support our coach 100 percent. It doesn't matter if there has been an apology or not, the decision has been made.
We think the coach's decision is correct but we believe we will receive offers for Orellana because he is a great player and we are already working on a replacement.
It is unknown if Hjulsager will be available to feature in the first leg, but he will be a credible threat once selected.
Celta will be expected to make it to the final, but two-legged affairs often raise surprising results.
Alaves average a goal conceded every match in La Liga, per Sky Sports, but it is their attack that might be their overriding weakness.
The visitors are not prolific, and they will struggle to score away from home.
The first leg will dictate how this fixture unfolds, and Celta will hope to place one foot in the final with a stellar performance on Thursday night.