Arsenal failed with an offer for the Spain U21 keeper over the summer, though remain keen on the Paris gold medalist.
Garagaza said: "He is a well-established asset of the club. There were movements in the summer, but I never considered selling him, which doesn't mean that it won't happen at another time.
"In fact, there is a need, but this summer was not the time. They called me after the match against Atlético in a serious way, but there was nothing to talk about. The boy had a bad time and had a few bad weeks. We had to explain things to him. It's clear that he's going to make the jump ."
On coach Manolo González, he also said: "Manolo is a club man. He is a natural, open person and very good at group management. He has a very important virtue: adapting to the situation. That tactical variety and ability to adapt depending on what needs to be worked on is basic.
"He has earned his place there. I was clear that he was ideal for the reserve team and for the first team. He is a coach with experience and he is doing very well."