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.
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.
On his arrival at Glasgow Airport on Friday, he said he was confident of his return being approved by the authorities, after settling a long-running dispute with the South African tax authorities.
King has since clarified he was referring to the approval of financial authorities, rather than the SFA.
When asked about King and a potential future role with the Light Blues, Regan told BBC Scotland: "There'll be mitigating factors and we're hypothesising.
"Article 10 tells us exactly what's allowed under 'fit and proper'.
"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.
"Until the process is kicked off it is very difficult for us to make any comment.
"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."
Regan met with King last summer and added: "He wanted to understand the process that had to be followed if he was to be considered (as a director).
"At the time he wanted to be involved in one of the consortiums (vying for control of Rangers).
"I set out to him what the process was and told him he would need to disclose fully anything he felt was relevant as far as Article 10 is concerned.
"What he has is an understanding of the process. What he hasn't had is any assurances from myself or any of my board or colleagues about any proposal for him to join the board."
Also speaking to BBC Scotland, King said: "I haven't even approached the SFA. The comments I gave when I arrived were in relation to the AIM requirements and were nothing to do with the SFA.
"But I'm certainly very happy, when the time comes and we've something to put towards them, that it'll be fine. We just haven't got to that point yet."
He added: "I've had a total of six meetings since I came here. All of the meetings have agreed to be private and confidential.
"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. I've had six meetings and each and every one has been a good and positive one, but we're not there yet."