Michel and Luis Enrique are leading candidates to replace Julen Lopetegui as Spain coach after the World Cup, according to reports.
On Tuesday, three days before Spain face Portugal in their first World Cup game, the Royal Spanish Football Federation (RFEF) announced that Lopetegui would take over as Real Madrid coach after his release clause was paid.
The former Spain international has been out of a job since being sacked by Malaga in January and has had coaching stints with Real Madrid's youth team, Rayo Vallecano, Getafe, Sevilla and Marseille.
His biggest success so far was winning two championships and the 2013 Greek Cup at Olympiakos before he was dismissed in January 2015. He was among the candidates to replace Vicente del Bosque as Spain coach in 2016.
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"Michel would have been a good option to coach Real Madrid and he is too, for Spain," Del Bosque told Onda Cero radio on Tuesday.
Luis Enrique, a reported target for Arsenal and Chelsea in recent months, has not coached since leaving Barcelona in May 2017.
A gold medal winner with Spain at the 1992 Olympics, he made 62 appearances for his country and has long expressed a strong interest in coaching them.
Lopetegui, who last month signed a two-year contract extension with Spain, took over after Euro 2016 and is undefeated so far.
"It's obvious that the news on Lopetegui is a surprise," Del Bosque said. "But I'm convinced the coach will do the same job for the national team. This is not going to affect the day-to-day of the national team."
Del Bosque added that he believed Madrid had found the ideal replacement for Zinedine Zidane. "I'm always inclined towards Spanish coaches," he said. "I think Lopetegui is ready to coach Real Madrid."