The scheduled meeting had taken on extra significance after Mackay's head of recruitment Iain Moody was removed from his post last week.
Moody was replaced by 23-year-old Alisher Apsalyamov, who is apparently a friend of Cardiff owner Vincent Tan's son, and has no known experience of top class football.
Chief executive Simon Lim was among those in attendance at the meeting, although Tan was not, but Sky Sports understands talks were positive and productive.
Mackay's agent Raymond Sparkes made it clear prior to the meeting that the former Watford boss was not going to quit his job.
But Mackay is understood to be very disappointed by the decision to replace Moody, who he had worked with since his time at Vicarage Road.
The 41-year-old is believed to be concerned at what the change of personnel would mean for the future of the club.
Meanwhile, Cardiff striker Craig Bellamy believes the club are worse off following the departure of Moody.
"Iain is a huge loss for us, a huge, huge loss because he is outstanding," he said.
"Any club with Iain Moody is a miles better club, without a shadow of a doubt."
Bellamy added: "As a manager, Malky is the best young British manager out there and what he's done for this club in a short space of time is nothing short of remarkable.
"That's not being disrespectful to the managers who were here before him but he's taken it on to another level.
"He's united the city and being from Cardiff that makes me feel very proud."