Mackay remains in charge of the Bluebirds following a lengthy board meeting on Monday.
The scheduled meeting had taken on extra significance after Mackay's head of recruitment Iain Moody was removed from his post last week and replaced by 23-year-old Kazakhstani Alisher Apsalyamov.
Apsalyamov is thought to be a friend of Cardiff owner Vincent Tan's son, and has no known experience of top class football.
Mackay will not resign from his post despite his disappointment and frustration over the loss of Moody, and the club have denied he was asked to leave his role.
But Mackay's position remains under scrutiny and his agent Raymond Sparkes has suggested he does not have the full support of some at Cardiff City Stadium.
The club's supporters' trust has again called for the Barclays Premier League outfit to provide a public explanation of the reasons for Moody's departure, and for them to consider having a supporter director.
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."