The French hitman is currently considering his options after slipping down Phil Brown's pecking order this summer.
Cousin joined from Rangers a year ago, but recent moves for Jan Vennegoor of Hesselink, Jozy Altidore and Kamel Ghilas has curtailed his playing time.
Cousin, who reportedly missed out on a transfer window move to Burnley still has two years left on the three-year deal.
However, his agent Willie McKay has hinted the 32-year-old would be prepared to play for Cardiff should Dave Jones come knocking.
"He's got a contract for a couple of years at Hull," he told the Hull Daily Mail.
"I wouldn't think that Daniel would want to move to a Championship club but Dave Jones at Cardiff is a good manager and always liked him when he was at Wolves."