The Elland Road side seem very keen to get rid of Barmby in order to further reduce their wage bill.
The Tigers would love to welcome Barmby to The KC Stadium, but his situation at Leeds is the main sticking point to any move.
Tigers boss Peter Taylor says that he would love to have Barmby in his squad, if he can find a way out of Leeds.
"We're hopeful and I'd love to have him here, he's a brilliant player," said Taylor.
"He's had a difficult time at Leeds because Terry Venables signed him and then Terry left.
"If Nick can sort out his situation at Leeds then we would be very keen to have him here because I admire him as a player and as a person.
"I have spoken to him a few times and I've known him a few years.
"He's from Hull so there is the Hull connection and he has got family here."
