The Dons chief claims a decision has yet to be made on how they will cast their vote in a general meeting of all 12 top-flight clubs on July 4. Hearts and Dundee United have revealed plans to reject Rangers' SPL bid, while Motherwell will ballot fans on the issue.
An 8-4 majority is required, with speculation mounting that Charles Green's newco could drop down to the Irn-Bru First Division - as opposed to the Third Division - should they fail to gain enough backing.
In a statement on the club's website, Aberdeen chairman Milne said: "Contrary to reports, AFC has still to reach a final decision regarding the 4th July vote on the Rangers newco.
"This is a critical decision which will have major implications for all clubs and the future of Scottish football.
"The views of our fans and the issue of sporting integrity will clearly be a major influencing factor in our decision-making."
The Dons announced a number of boardroom changes earlier in the week, including the departure of former player and manager Willie Miller as director of football.
Milne added: "There is a great deal of speculation about the future of the game in Scotland flying around at present, however I can categorically state that any rumours regarding AFC's financial position are ill-founded and completely wide of the mark.
"It is irresponsible for anyone to suggest otherwise.
"The changes announced earlier this week to the board and the executive are intended solely to significantly strengthen the club's position and help achieve our ambitious future plans."