The 27-year-old goalkeeper is a regular for Los Periquitos, and his fine form has attracted interest from the Premier League duo as well as the likes of Barcelona in Spain.
However, Casilla has no interest in a move away from the Catalan club, revealing he feels he owes his employers for standing by him.
"My intention is to stay here," Casilla told El Mundo Deportivo.
"This club gave me so much when things were going badly, and I always had a helping hand when I needed them.
"Now I am happy here, enjoying myself and playing. This is where I belong."
Casilla has another year left on his current deal, but is not concerned that another may not be forthcoming.
"Obviously I want to stay," Casilla added.
"I am staying here at least one more year so it is not alarming to me."