Cronulla called a number of its players and their managers to an emergency meeting on Tuesday night to discuss the club's mention in an Australian Crime Commission report into alleged doping.
At the meeting lawyer Richard Redman, a former ASADA senior counsel who's been hired by Cronulla, told the players they should voluntarily stand down for six months or risk ASADA's maximum two-year ban, News Ltd reports.
It's understood the players have 48 hours to make up their minds, and if they accept the ban they'll continue to be paid.
ASADA told Sharks officials and players this week of the extent of their involvement in the investigation, which focuses on the time sports scientist Stephen Dank spent at the club in 2011, although Dank has denied any wrongdoing.
Two peptide-based supplements given to Sharks players are reportedly of concern to ASADA.
Fairfax has been told players are considering legal action against the club, claiming they were told the substances were legal.
The Sharks are expected to address the matter at a media conference on Thursday.
The club sought to reassure fans with a short statement on its official website.
"Sharks fans and all rugby league supporters can be assured the club has been very proactive in fully co-operating with ASADA and taking other measures that prioritise the integrity of our club and the welfare of our playing group," it said.
As the crisis cast a pall over the NRL season start on Thursday night, bookmakers suspended betting on Sunday's Cronulla-Gold Coast game.