Jose Mourinho's side face the Basque side knowing the victory will be enough to guarantee them a first league title in four years and put a dent in Barcelona's recent dominance of Spanish football, no matter how the Catalans fare against Malaga.
But Europa League finalists Athletic also have plenty to play for with just three games remaining.
Marcelo Bielsa's charges may have seen their hopes of qualifying for the Champions League through a top-four finish effectively ended by their weekend defeat at Real Zaragoza, but they are still looking to ensure European qualification through the league.
They have also lost just one of their last 10 homes games, and Muniain is keen to spoil Real's party.
"It's a game which will require a lot from us," he told Marca. "They are playing for the league, but we always wear the shirt with pride and want to defend San Mames so there is plenty at stake.
"We know we will have to play a perfect match, against such world-class teams you have to leave everything on the field but this team is prepared to stand up."
But the 19-year-old admitted there is still a lingering disappointment over their costly weekend loss.
"It's a shame," he said. "It is complicated because Real are looking to secure the top spot, but we will try to get as high as possible.
"Let's go for all the remaining games and see if we get the most points possible to try and secure fifth place."
Mourinho will be without the suspended Angel Di Maria for the journey to Bilbao, with Jose Callejon set to deputise, while Sami Khedira could come back into the midfield.
And goalkeeper Iker Casillas says the time has come for the club to step out of Barcelona's wake and become the most powerful side in La Liga on a consistent basis.
"A team like Madrid cannot continue on any longer being a supporting act," Casillas told reporters. "We're a little tired of it and it looks like it's over. All of our work over these months, even years, is finally bearing fruit."