The Lions won the Supercopa de Espana last month and are still waiting to face Real Sociedad in last season's rescheduled Copa del Rey final, which is set to be held in April.
Levante have never won any major cups but will see this as a huge opportunity to change that given that they sit above Athletic in the La Liga table.
Athletic will consider themselves hugely fortunate to still be in contention for what could technically be back-to-back Copa crowns after surviving a big scare in the last round.
Raul Garcia scored a 94th minute equaliser for Athletic against Real Betis before the Basque side went on to win 4-1 on penalties.
Marcelino's side also played away in the previous two rounds, seeing off Ibiza and Alcoyano - the side that knocked out Real Madrid - by the same 2-1 scoreline.
Levante have had to come through five rounds to make it this far, most recently beating Villarreal 1-0 in extra time in the quarter-finals thanks to Roger Marti's last-gasp goal.
Including their cup victories, the Frogs are now unbeaten in nine matches since early January and are ninth in La Liga with 27 points.
That is two more points than 11th-placed Athletic, who played out a 1-1 draw with Valencia in their most recent league match.
The sides may be battling it out for a place in Europe next season, but for now both teams will be fully focused on progressing in the Copa del Rey.
The second leg of the tie is scheduled to take place at Estadio Ciutat de Valencia on March 4, with the winners over 120 minutes - or potentially more - to face either Barcelona or Sevilla in the final.
Athletic won 2-0 when the sides last met in the league four months ago - the Lions' fourth successive victory over Levante, each of those games in the league.
Athletic Bilbao Copa del Rey form: WWW
Athletic Bilbao form (all competitions): WWWLWD
Levante Copa del Rey form: WWWWW
Levante form (all competitions): DDWWWD
Influential midfielder Iker Muniain missed Athletic's draw with Valencia because of a knock and remains doubtful for this cup tie.
As for the visitors, Cheick Doukoure was back among the subs for the 2-2 draw with Granada on Saturday and could come into the XI here.
Athletic Bilbao possible starting lineup:
Simon; Lekue, Alvarez, Martinez, Berchiche; De Marcos, Garcia, Muniain, Berenguer; Villalibre, Garcia
Levante possible starting lineup:
Cardenas; Coke, Postigo, Vezo, Tono; Radoja, Malsa; Son, Rochina, Bardhi; Marti
We say: Athletic Bilbao 1-0 Levante
Athletic Bilbao, two points worse off than Levante in La Liga, will be looking to make home advantage count in this tough-to-call two-legged cup tie.
Marcelino's men have a good record in this fixture and tend to do well in domestic cup competitions, so we are tipping them to take a slender lead into the return match.