Fernando Hierro, Spain's director of football at the time, stepped in to take the reins over the course of the tournament, as La Roja were eliminated in the last 16 by Russian Federation in a penalty shoot-out after a 1-1 draw.
Former Barcelona coach Luis Enrique is set to be named as the new manager of the Spain national team, according to widespread reports in the country.
A great number of tasks are at hand for Luis Enrique when he begins life as the coach of the Spanish national team, with a select number dominating the fate of his tenure.
After a disastrous World Cup campaign, in which Spain only won one match - against Iran - Hierro decided against staying in the role and will not return to his old position as sporting director.
Spain, who won back-to-back European titles (2008, 2012) and the 2010 World Cup, are hoping to open a new successful chapter under Luis Enrique after three consecutive disappointing tournaments.
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A formal unveiling is likely to take place next week.
Rubiales added: "We have not spoken to anybody else - only Luis Enrique".
Rubiales also appointed former La Roja and Deportivo La Coruna goalkeeper Jose Francisco Molina as Spain's new sporting director. His first season started shakily while he searched for a settled lineup but ended in a treble of La Liga, Copa del Rey and the Champions League, beating Juventus in the final.