It is a re-run of the 2009 final, when Barca won 4-1 on their way to a six-trophy haul that year, and comes with them sweeping aside all challengers.
Their 5-1 thrashing of city rivals Espanyol on Saturday was a record 10th consecutive road win in the league stretching back into last season, and they are unbeaten in their last 22 matches.
They have scored 31 goals and conceded just one in their last seven outings, more than their Basque visitors have scored all season.
"It's one of those games where you could think we had nothing to lose," Bilbao midfielder Pablo Orbaiz told daily El Correo.
"No one can remember a side so far superior to others."
Bilbao, who are eighth in the league, will be without their top scorer Fernando Llorente who damaged a muscle in Saturday's 2-1 win at Levante.
Holders Sevilla are at home to Malaga on Wednesday looking to end a run of seven matches without a win, while Real Madrid host Levante.
"We will try to come away from the Bernabeu still alive in the competition," Levante coach Luis Garcia told reporters.
La Liga heavyweights Valencia and Villarreal clash in an east-coast derby at Mestalla on Tuesday and Deportivo La Coruna vist the only lower-league club left in the tournament, second division Cordoba, on Tuesday.
The second legs are scheduled for January 5.
