It is understood Mackay will not resign from his post immediately, despite seeing one of his most-trusted aides suspended and subsequently being placed on gardening leave, but the move has put his position under scrutiny.
Cardiff's Malaysian owner Vincent Tan has handed Moody's duties on an acting basis to 23-year-old Kazakhstani Alisher Apsalyamov.
Apsalyamov is thought to be a friend of Tan's son and appears to have no previous experience in football.
He joined the club in February but his name does not appear on a list of key staff members on the club's official website.
Tan previously caused consternation among Bluebirds' fans by changing the club's playing kit from blue to red and heavily altering their crest in 2012.
It has also been reported Tan asked Mackay to resign on Tuesday, Cardiff were unavailable to comment when contacted.
And the Supporters' Trust are concerned the club could lose their highly-rated and popular Scottish boss.
Chairman Tim Hartley said: "Fans will be concerned with the recent behind-the-scene developments at Cardiff City which appear to put into question the future of our manager, Malky Mackay.
"Supporters are surprised that who appears to have little hands-on experience has been put in charge of transfers at the football club.
"Fans want Malky Mackay, who has done a fantastic job as manager taking the club to the Premier League, to remain at Cardiff City.
"We don't want to see any action taken to undermine his position as manager and Cardiff City's efforts to have a successful first season in the top division.
"There are fears that the current developments could drive Malky into the arms of another Premier League club and that would be hugely damaging for the Bluebirds. Malky is a talented manager who has huge respect among the fans for what he has delivered.
"Fans deserve a clear statement on the position from the club on what has been happening and Malky's position needs to be made perfectly clear."