"The offer is wholly unacceptable, completely unrealistic for a player of his ability," Fuller told the club's official website.
"Only last week Albion agreed a deal with Crewe Alexandra for Rob Hulse which will add up to £1m and then they offer such a paltry fee for James.
"Three years ago they offered £750,000 for James, which we felt was insufficient then.
"He has since gained further experience and that needs to be recognised by West Brom," he added
It now looks certain that the matter will be settled at a tribunal.