The Blancos boss revealed that if the Welshman fails to find full fitness before the weekend, he will instead play the 20-year-old attacker at San Mames
The Wales international missed the Blancos' 1-0 win over Espanyol on Tuesday - which saw the capital club progress to the semi-finals of the Copa del Rey 2-0 on aggregate - after picking up a knock against Granada on Saturday.
Jese continued his fine form by scoring the one and only goal of the game at the Santiago Bernabeu and Ancelotti says the 20-year-old could keep his place in the side to face Athletic.
"If Bale is fit, he will play at San Mames, and if not, then Jese can play there," the Italian told reporters after the game. "He causes a lot of danger to the opposition.
"It will be a very difficult game. Athletic are playing well at the moment and San Mames is never easy. For us, though, it comes at a good time. We hope to win."
Real Madrid head into the Liga clash on the back of eight consecutive wins without conceding a single goal, after shutting out Espanyol at the Bernabeu.
Ancelotti mused: "We started well and controlled the entire game. Everyone had a good game, including Fabio Coentrao. Asier Illarramendi is starting to play with more confidence in his position, too.
"I'm happy. We're going to continue with this system as it gives everybody confidence.
"I think the record [also] gives us confidence. There is a defensive balance with us as the whole team works hard to get the ball back."