Mackay met the club's board for a scheduled meeting on Monday but discussions took on extra significance after head of recruitment Iain Moody was removed and replaced by an unknown 23-year-old - thought to be a friend of owner Vincent Tan's son.
Mackay's agent insisted he would not resign from his post, despite his frustration over the loss of Moody, and the club has denied the former Watford boss was ever asked to leave his role.
His position remains under scrutiny, however, and the Cardiff City Supporters' Trust now wants an explanation of recent developments.
Chairman Tim Hartley said: "Despite Monday'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, with Malky Mackay's agent now stating that he will make a statement if the club remains silent.
"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.
"We reiterate our support for Malky Mackay, who has been one of the best
managers in the club's history."