Villar, 67, was suspended from the post he has occupied since 1988 in September for a year after being arrested as part of a corruption investigation.
He was detained in July on allegations of collusion, embezzlement and falsifying documents and spent two weeks in custody before being released on bail.
However, the Spanish Sports Council's insistence that new elections be called for the presidency of the football federation has attracted FIFA's interest for political interference.
"All member federations have to administer their affairs in an independent manner and ensure that there is no interference from third parties."
Villar is also a former vice-president of FIFA and UEFA, but resigned from both posts following his arrest.
FIFA said on Friday that "a joint FIFA-UEFA delegation will be sent to Madrid shortly to monitor and assess the situation in the association".
"I can't contemplate this scenario. I am absolutely convinced that Spain will go to the World Cup in Russia and, moreover, they will win it," said Spanish Prime Minister Mariano Rajoy.
"I've heard about it, but I don't believe the offices will take from Spain what we have won on the pitch," insisted Spain captain Sergio Ramos.
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