With Barcelona not in action until Sunday, victory for the league leaders would give them clear breathing space ahead of El Clasico later this month.
Bilbao, however, will enter the match having lost just one of their last six in the league. Ernesto Valverde's side also booked their spot in the Copa del Rey final on Wednesday with an impressive 2-0 win at Espanyol in the second leg of their semi-final.
Last time out in the league, Bilbao won 1-0 at Eibar and they have conceded just twice in their last five games in Spain's top flight, with that run of form moving them into 10th position.
Since losing to Atletico Madrid, Real Madrid have won three of their four matches, but they were held to a 1-1 draw at home to Villarreal last weekend.
The capital outfit also have the best away record in the league this season - winning 10 of their 13 games and scoring 39 times in the process.
Incredibly, Real Madrid have won 17 of their last 19 league meets with Bilbao - losing just once. In terms of the more recent meetings, Los Blancos beat Bilbao 5-0 in the reverse league match earlier this season.
Bilbao boss Valverde has no fresh injury worries ahead of the match, with Ander Iturraspe their only major absentee. Markel Susaeta and Benat, however, should both return to the XI after sitting out Wednesday's match at Espanyol.
Real Madrid, meanwhile, are still without the services of Sergio Ramos, James Rodriguez and Luka Modric. As a result, Carlo Ancelotti is expected to stick with the same team that drew with Villarreal last time out.
Form in La Liga: DWLDWW
Form in all competitions: DDWLWW
Possible starting lineup: Iraizoz; Iraola, Laporte, Gurpegi, Balenziaga; Rico, Benat; De Marcos, Susaeta, Muniain; Aduriz
Form in La Liga: WWLWWD
Form in all competitions: WLWWWD
Possible starting lineup: Casillas; Carvajal, Pepe, Varane, Marcelo; Silva, Isco, Kroos; Ronaldo, Benzema, Bale
Sports Mole says: 1-3