Allegations surfaced last week in the New Statesman magazine that Mr Blunkett asked an official to check whether his son was affected by computer problems which hit exam marking in 1998.
Several former QCA officials were quoted over the weekend about the issue, recalling that the matter was discussed by the regulatory body at the time.
In a statement this week, Ken Boston, QCA chief executive, said:
"Neither myself nor other members of the current QCA executive were in post in 1998, and we have no recollection of any issues from seven years ago."
He said that if he were to discover that any minister had made personal approaches to the authority, he would declare so publicly. But Dr Boston added: "With regard to the events of seven years ago, I regard this matter as closed."
A former QCA management team member said that, practically, there was nothing to stop it investigating the issue by interviewing former staff members. But political considerations would have ruled this out.
The ex-official said: "Ken Boston could have held an inquiry. But I think he would have been very foolish if had he tried to. He would have been told (by the Department for Education and Skills and 10 Downing Street) that he was being extremely foolish to do such a thing."