Perez said there had not yet been any formal discussion about Del Bosque's future and it had been decided to wait until the team, who play their final match against Australia on Monday, was back in Spain before holding talks.
"It is better to let some time elapse and wait to discuss things calmly in Madrid," Perez said on Spanish radio.
"When Del Bosque signed the contract (to 2016) he said that if for any reason we thought he should not continue he would leave," he added.
"Del Bosque has not presented his resignation and if he did we would ask him to carry on.
"His family might convince him not to continue but we will not find anyone better.
"From the top to the bottom at the federation we are with Del Bosque. If we have the best why change?"
Del Bosque, 63, has already earned his place in the pantheon of football's greatest managers despite the unexpected setback in Brazil.
After taking over from Luis Aragones following Spain's Euro 2008 victory, he led the nation to their first World Cup triumph in South Africa in 2010 and a second straight continental title at Euro 2012 in Poland and Ukraine.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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