The Union of Fans wants the club to make an iron-clad promise not use the stadium and training ground as investment security.
It comes after former director Dave King met with the new League One champions' ruling regime to address concerns about club finances after last year's £14.4million loss.
On Saturday, the board promised the South African-based businessman it was determined to place Rangers at the forefront of Scottish football and said it had "no inten-tion" of using Ibrox or Murray Park as security.
A statement from the fans group said: "Although pleased that the [board] have made a commitment not to take out any type of security, on Ibrox or Auchen-howie, we are disapp-ointed they have refused to make this as unequivocal as we would have expected.
"'We have no plans' does not engender the same confidence as 'we will not'."
King said on Monday he'd give the board 30 days to complete chief executive's Graham Wallace's review of the club. The fans' group backed him saying: "The board's position has changed over the weekend, from one where we had no clear sight of their strategy with regard to moving the club forward, to one where they have now committed to fans and shareholders to implement the funding plan we believed was required."
King had suggested if the fans wanted more say in how the club was run, they should set up a trust to collect season-ticket cash and drip feed it to the club.
The Union of Fans says it expects to launch such a scheme soon.