Speculation has raged over the future of Mackay after Cardiff owner Vincent Tan placed the club's head of recruitment, Iain Moody, on gardening leave last week.
Moody – who worked closely with Mackay in his previous job at Watford – eventually left the club, replaced by 23-year-old Alisher Apsalyamov, reportedly a friend of Tan's son.
Mackay was alleged to have been unhappy with the situation and attended a board meeting on Monday to discuss the matter.
But the manager's agent, Raymond Sparks, says that the chances of Mackay walking out on the club are non-existent.
When asked if there was a chance Mackay would be quitting, Sparks told BBC Radio: "No, absolutely categorically not. Even now that's not something Malky is contemplating.
"There is absolutely no prospect of Malky resigning from a job that he loves, a job he's ensconced in."
Mackay led Cardiff – who sit 14th in the Premier League table - to the Championship title last season.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.