The full-back is being investigated by the governing body over an alleged abusive remark in last Friday’s 13-12 defeat to St Helens.
It is claimed referee Richard Silverwood heard a comment during the match and Hardaker - handed a five-game ban in June after being found guilty of homophobic abuse during Leeds’ fixture at Warrington - is now under mounting pressure.
The RFL have employed the services of a lip reader to aid their investigation when reviewing television footage.
But Leeds chief executive Gary Hetherington said: “We are concerned there appears to be a witch-hunt by the RFL towards Zak Hardaker and we are calling for an external investigation into the issues surrounding the investigation. “We know the Match Commissioner was asked by the media at the post match press conference if the Referee had reported any incident or comment and they were told ‘No’.
“We want to know why the Referee’s report quite mysteriously now contains a reference to a possible comment.
“It seems incongruent with the RFL’s stance and the vigour that they are now pursuing this incident with that the referee would not have reported this to his superior on the night, as is the protocol in these circumstances, or taken action during the game.
“We understand a St Helens player has been interviewed and he has stated he did not hear anything.
“There is a hint of mystery about the whole issue and the use of a lip reader has added a new dimension to on-field conduct, particularly when games are televised.
“We also want to better understand why the RFL are pursuing this so rigorously.
“The only person who appears to have heard anything at all is the Referee and he has belatedly reported this despite not taking any action on the field or after the game with the match commissioner. We want to know the timeline and those involved in this process.
“Given that no charge has been made, it is remarkable that Zak’s name was released to the Press Association by an RFL spokesman on Tuesday and this just adds the doubt behind the whole process.
“The duty of care from the governing body to an individual under investigation is surely paramount.
“The RFL’s guidelines state that the burden of proof lies with the RFL and anyone under investigation is innocent until proven guilty.
“Whilst the RFL deliberate and we will continue to support Zak and at the same time press the RFL for clear transparency about the whole process.”