Vicente Del Bosque says he would be willing to leave as Spain coach, however the Spanish Football Federation wants him to continue.
But Jorge Perez, Spain's director of football, told Spanish radio: "If he does resign, we will try to convince him to stay."
Del Bosque said: "If I am a problem for our football, I will go."
He added: "The interests of the national team and the Federation will rank above my own interests when I make my decision.
"But the reality is what it is and, as far as it's up to me, I want to do what is best for the national team.
"If they had told me that we would be in this situation before we arrived [in Brazil], considering how the players were training and how focused they were, I would have thought it was impossible."
However, Perez said that the federation would wait until after Spain's final game against Australia to discuss Del Bosque's future.
"We still haven't spoken with Del Bosque, it's better to put a bit of distance between us and wait and then speak calmly in Madrid," he said.
"His family might convince him to leave, but we aren't going to find anyone better."
Del Bosque was also criticised for selecting Real Madrid goalkeeper Iker Casillas, who made crucial errors in both games as Spain conceded seven goals, while scoring just one.
But Perez's public backing paves the way for Del Bosque to remain as head coach as Spain attempt to win a third successive European Championship title in 2016.
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