The Portugal international forward has been training alone in the build-up to the fixture as he struggles with an Achilles problem.
Ronaldo suffered the injury in Wednesday's 2-1 victory at Ludogorets in the UEFA Champions League following a hefty challenge from Anicet Abel.
The 29-year-old, who missed and scored a penalty in the fixture, was left fuming afterwards, likening the contest to a rugby match.
Real will be desperate for Ronaldo to play and continue his sensational start to the season, which has seen him score 10 goals in just five league outings this season.
With or without Ronaldo, Real will be confident of picking up all three points having beaten Bilbao in their last nine league encounters at the Bernabeu.
Three out of the last five of those contests have finished 5-1 and Carlo Ancelotti's men head into the contest on the back of a five-match winning run in all competitions.
One area Ancelotti has been unhappy with, though, is Real's defending from free-kicks and corners after conceding from a set-piece against Ludogorets.
In the aftermath of that win, he noted: "The start wasn't good and conceding again from a set-piece could have made things complicated.
"But the reaction was good. The team played well in attack and we're physically very good at the moment."
Ancelotti must once more make do without full-back Fabio Coentrao, forward Jese Rodriguez (both knee) and midfielder Sami Khedira (thigh).
For Bilbao, the trip to the Bernabeu could hardly come at a worse time.
Ernesto Valverde's side enjoyed an excellent campaign last term, which saw them finish fourth in La Liga.
However, Bilbao have endured a miserable run - failing to win in their last six competitive outings, with their misery compounded by a surprise 2-1 setback at BATE in the Champions League on Tuesday.
With just one Liga win to their name this term, a rare victory at the Bernabeu would prove a timely boost for Bilbao ahead of the international break.
Attacking midfielder Isaac Aketxe is Bilbao's only reported injury for the clash - the 25-year-old is suffering with a toe injury.
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