The South African-based businessman flew into Glasgow on Friday for a series of talks with both current Ibrox directors and the group of prominent shareholders seeking changes to the board.
But Regan has told Dave King he would be "a little premature" in believing he would have no issues with returning to the Rangers board.
King - a former director who invested heavily in the Sir David Murray era - has had discussions about the possibility of a return to the Glasgow giants, as well as possible reinvestment.
When asked about King and a potential future role with the Light Blues, Regan said: "We have had no contact from Rangers or anyone else regarding Dave King. As far as we are concerned, any suggestions that he has no issues as far as the SFA's fit and proper test is concerned is a little premature.
"I spoke to [director] Brian Stockbridge last night and he assured me that as far as the club is concerned there is no discussion on Dave King's fit and proper requirements.
"You need full disclosure of the facts and that requires the club to lay those out to us, if they believe there are issues the PGB need to consider.
King admitted he had not approached the SFA to discuss the fit and proper criteria
He added: "I've had six meetings since I came here. All of the meetings have agreed to be private. But I regard each of them as very constructive in what I'm hoping to achieve. I think it would be premature of me to speculate that I'm there yet."