Sharks coach Shane Flanagan said his players were on board with the idea.
"As a club, we've challenged ourselves -- how can we help in this area?" Flanagan said yesterday.
"Is it a problem in the game? I'm not quite sure, but we want to set some examples as a club.
"They say it's a society problem; you can't have it in rugby league.
"Hopefully we can all work together to come up with a system that doesn't allow this to spoil our game."
It's not the first time the NRL has faced calls to green light hair follicle testing.
In 2015, then South Sydney chief executive John Lee raised the idea after players Dylan Walker and Aaron Gray overdosed on painkillers.
Sports Lawyer principal Paul Horvath, a Melbourne solicitor with expertise in drugs in sports, said hair follicle testing had the potential to provide a higher degree of accuracy than other forms of testing.
But he agreed with the RLPA that players' privacy could be put at risk.
Horvath said the testing was intrusive and could result in, for example, the unwanted revelation of a player's issues with mental health.
"The recent problems with the [former] Cronulla chairman are concerning in terms of setting the cultural tone of expectations within an organisation and no doubt Cronulla are seeking to clean that up," Horvath said.
"The type of sensitive and personal information that's acquired by the employer in testing hair follicles and the sorts of substances that can show up there has serious privacy implications.
"It's my view that the more appropriate channels for the introduction of hair follicle testing is through the players' association in conjunction with the NRL.
"The deterrence should be something that's across the board in the NRL, rather than being sought to be created within one club."
- AAP