New Barca boss Ernesto Valverde is reportedly keen to bolster his midfield options, with Paris Saint-Germain's Marco Verratti thought to be on top of his wish-list.
Atleti star Saul, who scored a brilliant hat-trick as Spain beat Italy 3-1 to reach the European Under-21 Championship final on Tuesday, has been mentioned as a possible back-up should Barca fail to land Verratti.
However, Saul is planning to remain in the Spanish capital with Atleti for the foreseeable future.
"I have no intention of moving," he told AS.
"I'm where I want to be and things are going to remain the same.
"They [Atletico] have put their trust in me since I was young, and I want to repay that confidence."