The Bluebirds have seen two bids for Premier League players rejected in recent days as they look to strengthen their injury-hit squad, but Mackay has revealed that will not deter his efforts to improve his side.
Mackay said: "We have spoken to a couple of Premier League clubs already and unfortunately been knocked back for a couple of players.
"Clubs have their own situation with players - with the Capital One Cup, or being short of players and being exposed due to injuries - and cannot move them.
"We will continue to look to see if we can get some cover for the next month."
Cardiff are currently sitting in second place in the Championship table.