The timing is also unexpected as Spain kick off their World Cup campaign on Friday when they take on Portugal at the Fisht Olympic Stadium in Sochi, Russia.
The 45-year-old was quickly linked to taking over his nation, who under Didier Deschamps are considered among the World Cup favourites.
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Zidane, who scored twice in the 3-0 final victory over Brazil in 1998, was talking on the eve of a gala match pitching the World Cup-winning French team, minus then-captain Didier Deschamps who is now in Russian Federation with the France team, against an worldwide XI to mark the 20th anniversary of France's win.
With Spain, he has won 14 and drawn six since succeeding Vicente del Bosque in 2016.
Lopetegui's playing career included a spell at Real, although he made just one appearance and was mainly loaned out to Las Palmas. He has previously coached Spain's youth sides and had two years in charge of Porto.
It remains to be seen if he will head to Real as a World Cup victor, though Spain's squad is stocked with exciting talent.
In the meantime, Madrid may have to wait until mid-July before they can begin to work with their new coach - which is extremely late in terms of planning transfers and shaping the squad in time for the start of next season.