Aguirre has been implicated in a match fixing scandal from when he was the coach of La Liga side Real Zaragoza, however, the Japanese Football Association (JFA) will stand by the coach for the time being.
Aguirre is expected to appear in court in Valencia next month over claims that he was involved in a major match fixing incident in 2011.
JFA chief Kuniya Daini said: "When the initial report that the court case had been accepted came out, usually in these situations the report tends to be right.
"We are checking every day to see if the case has been accepted or not and so far we have not been able to confirm it and we are sticking with Aguirre.
"Once we know for sure whether it has or has not been accepted we will explain our position. From our point we are praying that the case has not been accepted."
Defending champions Japan were dumped out of the Asian Cup by UAE on penalties, with stars Keisuke Honda and Shinji Kagawa both missing their penalties.
Honda, who plays for AC Milan, said: "I can't turn back time. Maybe there's a reason why I missed."
"It's a harsh reality. It shows we were perhaps a bit naive in not being able to cope with the pressure to win the tournament.
"I said it after the World Cup too but we weren't prepared for such a tough game. Mentally we were not able to adjust."
"I've seen big players miss penalties on TV and it hurts that I'll be remembered for it now too. I tried to hit it hard but I just didn't catch it right."