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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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