The Mexican has been implicated in a match-fixing scandal that took place when he was the manager of La Liga club Zaragoza, and he will have to appear in court to testify later this year.
The Samurai Blue are currently doing well in their title defence at the Asian Cup, and authorities have decided to wait until after the competition to address the matter.
JFA president Kuniya Daini said: "Last night it was reported that the case involving Aguirre had been accepted by the court. We are trying to confirm whether that is official or not, and as yet we haven't been able to do so. We can presume from the details that it is true.
"We have discussed what we as a federation should do, and we have decided that the priority should be on allowing the team to concentrate solely on defending its Asian Cup title. The matter is closed for now, and I hope you understand.
"Once the Asian Cup has finished, then we will explain how we will respond. We are still gathering information and we have not decided anything yet. We will give priority to the Asian Cup, and then we will decide."
JFA attorney Yutaka Miyoshi added: "The case has been accepted by the judge in Valencia and now a full investigation will begin. That does not mean he will be prosecuted. An investigation will now begin, and once that has taken place, the decision will be taken to prosecute or not. In Japan, the likelihood of him being prosecuted at this stage would be 99.9 percent, but Spain has a different system.
"This is the first match-fixing case in Spain, so it's difficult to accurately say how likely it is that there will be a guilty verdict."