"There are clubs expressing an interest in Lee and a great deal more than the ones that have been quoted," said York boss Chris Brass.
"Lee is aware of it and we are keeping him in the picture. If Cardiff turn around and say they want him then we have agreed a price so there would not be a problem.
"Equally, if they turn around and say no he can then talk to other clubs who I'm sure would meet our asking price."
Bullock goes away on holiday this Friday and is hoping to have sorted a deal with Cardiff before he goes.