Villar is a vice president of FIFA and has been a member of its executive committee since 1998. He is also a vice president of European governing body UEFA and joined its executive committee in 1992.
The 65-year-old former Athletic Bilbao and Spain player is seen as close to FIFA's Swiss president Sepp Blatter, who has been at the centre of a corruption scandal prompted by U.S. and Swiss investigations.
Both Blatter and his UEFA counterpart Michel Platini, a Frenchman, have been provisionally suspended for 90 days by FIFA's Ethics Committee.
The suspensions followed reports of a payment of about $2 million from FIFA to Platini in 2011, nine years after he completed a spell working for Blatter as an adviser. Blatter and Platini deny wrongdoing.
Miguel Cardenal, the president of Spain's sports council (CSD), told Spanish television broadcaster Telemadrid on Wednesday Villar should state what he knew.
"It's something he needs to explain himself, nobody can give an opinion in his name," Cardenal said when asked if Villar was aware of any corruption at FIFA. "And I think it would be a good thing if he did so."
Many people had questions about Villar's position, he said.
"In the past he has made statements supporting his fellow members of the (FIFA) executive committee, assuring that there was no doubt about their honour.
"Time showed that his assessment was wrong and obviously he is the one who should explain this."
Neither Villar, who has not been implicated in any wrongdoing, nor the RFEF have made any public comment on the U.S. and Swiss investigations.
An RFEF spokesman told Reuters on Wednesday Villar would not be responding to Cardenal's demand.
Javier Tebas, the president of Spain's professional football league (LaLiga), also weighed in on Wednesday when he was asked at an event in Madrid about FIFA and Villar.
"Either Villar was very clever or very stupid if he did not notice anything," Tebas said.
"It worries me that the RFEF president did not notice anything that was going on."
Spain is one of a number of federarations now facing questions domestically.
Scandal engulfed FIFA in May when U.S. prosecutors indicted 14 football and marketing officials in the biggest corruption inquiry to hit the organisation in its 111-year history. Switzerland's Office of the Attorney General is conducting a parallel investigation.
(Reporting by Iain Rogers, editing by Angus MacSwan)
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