The Cardiff City Supporters' Trust wants the club to fundamentally change its approach, with the body calling for a representative on the executive and greater transparency as the uncertainty surrounding Malky Mackay's position as manager continues.
Following a board meeting on Monday, Mackay's agent, Raymond Sparkes, said the manager would not resign but admitted the Scot could yet be sacked by Vincent Tan, the owner.
With Cardiff still to comment on the board meeting, the trust issued a statement.
Tim Hartley, the chairman, said: "Bluebirds fans deserve a full explanation following the board meeting, including the reasoning behind the decision to appoint Alisher Apsalyamov as acting head of recruitment. The events of the last week at Cardiff demonstrate the need for a new approach to the ownership and governance of professional football clubs.
"Cardiff could make a start by acting in a more transparent way and by engaging and communicating with fans. It could also consider having a supporter director who would be able to represent the fans views at the top table.
"Despite yesterday's lengthy board meeting supporters are still concerned about the long-term future of our manager. There is confusion over the departure of Iain Moody [the former head of recruitment] with Malky Mackay's agent now stating that he will make a statement if the club remains silent.
"We reiterate our support for Malky Mackay who has been one of the best managers in the club's history."