Gerardo Martino's men were held to a 1-1 La Liga draw at Levante on Sunday but stayed top on goal difference after Atletico Madrid also dropped points, with Real Madrid a point further back.
Loukas Vyntra put Levante ahead in the 10th minute, but Gerard Pique earned Barca a share of the spoils with his first league goal of the season.
The draw was the first time in six meetings that Levante have avoided defeat to Barca - a far cry from the 7-0 thrashing dished out at Camp Nou in August - and Joaquin Caparros will be hoping it gives his players a confidence boost ahead of their first-leg clash at home.
However, Barca are the most successful team in the competition's history, with 26 triumphs, and have conceded just once in their four Copa del Rey outings this season, comfortably beating Cartagena and Getafe home and away.
Holders Atletico continue their defence against 23-time winners Athletic Bilbao.
Atletico host the first leg on Thursday and have won their last four home matches against Bilbao, with the visitors scoring only once, while Madrid have found the net 11 times.
When the sides met earlier in the Liga season, Diego Simeone's men ran out 2-0 winners and will be expected to reach the last four.
Bilbao beat Real Betis in the previous round, but could be hampered for the first leg given that they play Real Valladolid in La Liga on Monday before heading to Madrid three days later.
A repeat of last season's final will happen in the semi-finals if Atletico can defeat Bilbao and Real Madrid progress past Espanyol.
Carlo Ancelotti's side travel to Estadi Cornella-El Prat on Wednesday, a ground they won 1-0 at on January 12.
Pepe grabbed the only goal of that game and Madrid have since continued their impressive form with wins over Osasuna in the Copa del Rey and Real Betis in the league, thrashing the latter 5-0 on Saturday.
Madrid have now recorded seven consecutive wins in all competitions and have not lost since October.
Espanyol, in contrast, have only won six of their last 19 matches in all competitions, but come into the first-leg encounter after back-to-back victories over Alcorcon and Celta Vigo.
Third-tier Racing Santander, the only club outside of the top flight remaining in the competition, travel to Real Sociedad.
Santander beat Almeria in the previous round and also knocked out Sevilla.
Next up are out-of-sorts Sociedad. The Liga side have won once in their last four games to hamper the club's top-four hopes.
Copa del Rey success would be a welcome distraction, but Santander are top of Segunda B Group 1 and are nine games unbeaten in all competitions.
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