Latest reports claim that both Mackay and his players are outraged at the suspension of head of recruitment Iain Moody, who worked with Mackay at previous club Watford.
Moody was originally told on Wednesday that he had been suspended pending an investigation into his activities during the transfer window, but later that day was told he had been put on gardening leave.
The negotiator has been temporarily replaced by Kazakh Alisher Apsalyamov, according to newspaper reports, a friend of Vincent Tan's son and a man understood to have no experience in professional football.
Apsalyamov had been on a work experience placement at Cardiff during the summer, where his duties included painting the stadium.
The BBC have reported that Cardiff have not asked Mackay to quit, while Sky Sports News reported that Mackay has "no intention of quitting" over the row - despite the astonishing chain of events which appear to have undermined his role as Bluebirds manager.
Tim Hartley, chairman of the Cardiff City Supporters' Trust, issued a statement: "It is a surprise to all City fans that Iain Moody has been suspended and it is a pity because he has brought in top players like Steven Caulker and Gary Medel.
"We don't want any change to affect stability at the club. We made a good start to the season and it's important not to unsettle the players or the management team.
"We don't know much about Alisher Apsalyamov, but it appears he is only 23, and we don't know what football experience he's got. We understand from his own website that the new man is a friend of Vincent Tan's son.
"The recruitment of players has been a great success under Malky Mackay so at 23 we could be asking what experience Alisher Apsalyamov has got and, especially, of the British game?
"We're not concerned as yet, we just don't want anything to unsettle the present set-up."
Moody had worked with Mackay, who joined Cardiff in 2011, in bringing in a number of high profile acquisitions in the close season as the Welsh club broke their transfer record three times ahead of their first season back in the top flight in 51 years.
The pair's signings, including England defender Steven Caulker and Chilean midfielder Gary Medel, have helped Cardiff to 14th place after seven games following victories over Fulham and big-spending Manchester City.
Cardiff are yet to officially comment on the reports and Moody is still listed in his role on the club's website. The transfer window opens for clubs on January 1.
WalesOnline reported that Cardiff Chief Executive Simon Lim balked when quizzed if the manager had been asked to resign after speculation rose about his future following Moody's removal.
It added that Apsalyamov had described himself as having no previous experience in football prior to joining the club in February as executive assistant to Lim.
The Daily Mail said Apsalyamov had attended the same Swiss school as the son of Cardiff owner Vincent Tan and that the Kazak had been painting walls at the club's stadium three months ago.
While Tan's three-year tenure in the Welsh capital has brought success, his leadership has irked many of the fans.
The Malaysian billionaire, the former chairman of conglomerate Berjaya Group, has changed the Bluebird's kit from blue to red and switched the crest to include a dragon.
Tan has often gone on the offensive about the lack of gratitude towards him from supporters.
"I'm disappointed that after 51 years of not being in the top flight that there are still some fans who don't think we have done a good job. I may say maybe they are not grateful," he said prior to the start of the new season.
But it is not just the supporters who are frustrated by the actions of the owner, frequently photographed at matches wearing a replica Cardiff shirt over his shirt and tucked into his suit trousers.
A number of media reports said Tan was barred from entering the dressing room by Cardiff players prior to Saturday's 2-1 home defeat by Newcastle United due to a row about bonuses.
"I don't want there to be any perceptions of unrest behind the scenes, as we all know the job of Premier League survival is hard enough for a newly promoted club without added distractions and off-field issues," Tan said.
"Yes, things change at football clubs, much like they do in all organisations and businesses, but we carry on and do the best we can for the good of the club, which God willing for Cardiff City is to remain a Premier League club for as long as possible. That's our goal."