Mackay is trying to boost his squad following recent injuries to Andrew Taylor, Ben Turner and Aron Gunnarsson.
They join a number of other senior players on the sidelines including Craig Bellamy and Tommy Smith, and the Bluebirds chief revealed he has had numerous approaches rejected by a number of top-flight clubs.
"We have spoken to a couple of Premiership clubs already and unfortunately been knocked back for a couple of players," Mackay told BBC Sport.
"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."