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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.