The Brazilian international has been strongly linked with a move away from the Camp Nou in recent months as the Catalan outfit actively seek a new right-back.
Enrique has said that Alves remains with the squad 'for now', but failed to clear up the player's long-term future.
"I've said this several times. He arrived late in the squad [after the World Cup] but he has an animal level of fitness," Enrique told reporters.
"Alves is at Barca, he is in the squad and there he will remain. In the future, we'll see. I have opportunities to meet with anyone."
Sao Paulo defender Douglas has been strongly linked with Barca as a replacement for Alves.