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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.