The Bluebirds have turned to the Scot as they search for a replacement for Dave Jones, who was sacked at the end of last season. However, Watford have denied City permission to talk to the 39-year-old, who has impressed on a shoestring budget in his two seasons at the helm.
"We don't want Malky to leave Watford and we will do everything in our power to keep him at Vicarage Road," said new Hornets owner Laurence Bassini.
The development comes just hours after former Newcastle and England striker Alan Shearer revealed he had held "unsuccessful" talks over the vacancy in south Wales.
Chris Hughton and Roberto Di Matteo have been linked with the role but are also thought to be on the shortlist for the Birmingham job.
Mackay guided the club to 14th in the Championship last season.
Source: PA
Source: PA