News Ltd has reported that "sources close to the club" believe ASADA is trying to arrange to have some players stood down immediately for six months.
News Ltd understood that ASADA had told Sharks officials and players this week of the extent of their involvement in the investigation, which focuses on the time sports scientist Steve Dank spent at the club in 2011, although Dank has denied any wrongdoing.
Sharks coach Shane Flanagan had declined to comment on the current situation, but denied any Sharks players were interviewed by ASADA.
Meanwhile bookmakers reacted promptly to the swirling speculation.
"There's a lot of rumour and innuendo, particularly about one side, the Sharks," Tattsbet's Gerrard Daffy told AAP after his agency suspended games betting and a number of its futures markets at 4.30pm AEDT.
"There's rumours a lot of players are going to be stood down, and not all from the one one club."
Sportingbet Australia spokesman Bill Richmond said his agency had also stopped betting on the Sharks-Titans game.
"We stopped all markets associated with the Sharks game," Richmond said.
"We have calls from people already wanting to back the Gold Coast."
News Ltd said Cronulla had hired a top lawyer to help them deal with the ASADA matter.