Gayle has fallen out of favour at Palace, with Alan Pardew regularly opting to overlook the rapid front-man since taking over, and Cardiff believe that he could be available for transfer in the near future.
The Bluebirds have endured a disappointing campaign this season, where they were only able to claim a mid-table place, and they are determined to strengthen in the coming months.
The addition of Gayle would be a signal of their promotion ambitions and he would considerably improve their striking options.
The 24-year-old striker has finished as Palace's top-scorer across all competitions for two seasons running now and has already shown his class in the Championship.
Gayle made his name at Peterborough United, where he tore apart defences across the second-tier, and he will be hoping to have a similar impact at the Cardiff City Stadium should he move to the Welsh club.
If Palace did opt to sell it would come as a slight surprise, as Gayle has shown signs of promise during his time at Selhurst Park, but they may feel that the opportunity to recoup such a large fee for a player who isn't a guaranteed starter is too good an opportunity to turn down.