Real and Barcelona, who are the two most successful clubs in Spanish football, are among the seven clubs the Commission is probing, alongside top-flight sides Valencia, Athletic Bilbao, Osasuna and Elche.
Segunda Division side Hercules are also under investigation as the Commission seeks to determine if state aid received by those clubs is in line with European Union regulations.
Quoted in AS, Barca president Sandro Rosell on Thursday said: "We have not received any help from any official government agency.
"And Barca complies with the Spanish legislation which says an entity does not have to become an public limited sports company if it is in good health."
The Commission will also investigate whether the widely-reported land transfer between the City of Madrid and Real Madrid in 2003 involved any state aid in favour of the club.
Real president Florentino Perez told Desayunos Deportivos de Europa Press: "In regards to our business with the Ciudad Deportiva (Sports City training ground), there was a complaint and a subsequent investigation.
"They wanted to hurt us but nothing happened."
Spanish sport minister Miguel Cardenal, meanwhile, criticised European Commissioner Joaquin Almunia, who detailed the specifics of the investigation in Brussels on Wednesday.
Quoted in AS, Cardenal said: "There is no special aid plan, perhaps they would do well to study Spanish legislation. This has been very damaging to the image of our football.
"I have been especially interested in the matter of the taxation of the four clubs who are not public limited sports companies (Real Madrid, Barcelona, Athletic Bilbao and Osasuna) and I have looked closely at their tax details for the last four years. The potential benefits amount to 100,000 euros per team per year.
"Commissioner Almunia should clarify this. Saying that there's help from the state is ridiculous. I would ask why he has called a press conference on the European stage over such a trivial amount."
The president of Spain's Professional Football League (LFP), Javier Tebas, told Marca: "Spanish football is in question because we win a lot of titles and that becomes attributed to aid, when there is none.
"I don't know the situation surrounding the Valencian clubs too well but in terms of Real Madrid and the Ciudad Deportiva, there was a complaint filed years ago and those files are now in the archives."
Should the Commission adopt a 'negative decision' at the end of the investigation, it can order the member state, in this case Spain, to recover aid that has already been paid out from the beneficiaries.
Where the decision concerns existing aid, the Commission cannot order the recovery of aid already given, but will prevent the member state from granting future aid.
A Commission statement released to Press Association Sport read: "The aim of recovery is to remove the undue advantage granted to a company (or companies) and to restore the market to its state before the aforementioned aid was granted. There is a limitation period of 10 years for recovery."