The player's agent, Willie McKay, confirmed Cousin may have no choice but to leave Hull in search of regular first-team football.
"Unfortunately Daniel is not figuring for Hull at the minute and like every player he just wants to be playing," said McKay.
"Daniel is a good professional and he is working hard in training, but it appears he is being frozen out of things.
"I have some options for Daniel if Hull decide they do not want to keep him.
"One of those options could be for Hull to pay up the remainder of his contract and let him leave.
"If Daniel does leave he would like to stay in the UK as he enjoys the football here."