Athletic Bilbao are one of the teams alleged by a representative of "several European clubs", in a complaint filed in 2009, to have benefited from unfair tax advantages along with Pamplona-based Osasuna and the world's two richest clubs by income, Real Madrid and Barcelona.
The fact that Spaniard Almunia, who has been commissioner since 2010, is a Bilbao fan and was a minister in the government that signed off on the tax rules could imply a conflict of interest, said Ombudsman Emily O'Reilly whose job is to address complaints about maladministration in European Union bodies.
The Commission typically has 12 months after a complaint is made to decide on the opening of proceedings and in this case more than four years had passed without any action.
"Not only is this bad administration but to the European public it can look like a conflict of interest given the Commissioner's strong links to one of the football clubs in question," O'Reilly said in a news release.
"In my inquiry I have not looked into the merits of the allegations concerning the breach of state aid rules," she added.
"I trust, however, the Commission will decide to open an investigation tomorrow (Wednesday) in order to investigate the facts and dispel any suspicions."
O'Reilly added Almunia's office had informed her that a decision to open a formal investigation over the tax benefits will be on the agenda at a meeting on Wednesday.
Reacting to the Ombudsman's comments on Tuesday, Antoine Colombani, European Commission spokesman for competition policy, said Almunia considered it "unacceptable to suggest there could be any conflict of interest in this case".
Bilbao-born Almunia, 65, is a former head of Spain's opposition Socialist party and was a candidate for prime minister in the 2000 elections won by the conservatives.
"The point is on the agenda of the Commission tomorrow and this is obviously not because of the decision that the Ombudsman took today," Colombani said.
"We were in contact with the services of the Ombudsman and they were well aware that a decision would be coming."
Colombani noted that the Commission received "around 300 complaints" per year and they were "well aware that it sometimes takes us too long" to deal with them.
"We are working to improve the handling of complaints," he said.
The complainant in the Spanish soccer clubs case alleged that Bilbao, Osasuna, Real and Barca had enjoyed favourable tax treatment amounting to "several billion euros", O'Reilly's office said.
A spokeswoman declined to identify the complainant or the "several European clubs" they represented, saying the information was confidential.
Spanish Foreign Minister Jose Manuel Garcia Margallo announced on Monday that the Commission was poised to begin infringement proceedings against a total of seven Spanish clubs over possible illegal state aid.
The complaint against Barca, Real, Osasuna and Bilbao stems from the fact they are the only Spanish top-flight sides still owned by their members, or socios, and therefore receive more favourable tax treatment, Margallo said.
The Commission was also probing Real over the terms of the sale of their former training ground and Bilbao over aid they received for the construction of their new stadium which opened this season.
Valencia, Elche and Hercules were being investigated because of help the three cash-strapped clubs received from the regional government in the form of loans and bank guarantees.
Margallo denied the clubs had broken European Union rules and said the Spanish government, which will have a month to respond to the allegations, would attempt to prevent them being forced to pay back any aid.