Zaha has only made one start for United this season and could leave Old Trafford on loan in January.
Mackay said: “He is someone the whole world was linking with us over the summer because we were trying to spend some money.
“In January, we will see if there is anything available but if a player is to come in on loan they will have to be extra special, otherwise there is no point in signing these guys.”
Cardiff will face competition from a host of clubs looking to sign the 20-year-old winger.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?