Premier League rivals Norwich had been weighing up a move for the 29-year-old Frenchman.
Now Bluebirds boss Ole Gunnar Solskjaer is now ready to hijack any potential deal and bring the player to South Wales.
Ciani, who made a big impression at former club Bordeaux, made a big-money move to the Serie A club last summer.
However, the 6ft 3in centre-back has failed to make much of an impression under head coach Edoardo Reja.
Ciani has made 17 appearances in Serie A this season, scoring one league goal against AC Milan in October.