It has been reported by Wide World of Sports on Sunday afternoon that Asiata will either need to be vaccinated, or terminated by the club.
It's understood the club served Asiata a notice of termination last week.
What isn't clear is whether the proposed Rugby League Players Association policy - allowing players to be first docked pay for missed training or games, and then terminated eight weeks after a direction to vaccinate has been received - has been passed yet.
Asiata in the last few weeks became one of a handful of NRL players to speak out against the vaccine, reportedly telling The Daily Telegraph he would rather move into construction that become vaccinated to continue his NRL career.
It's understood there are only around 20 players across the entire competition who remain unvaccinated.
The NRL have refused to mandate the jab for players at this stage, however, issues stemming from restrictions for players to enter stadiums in Queensland and Victoria (as well as New South Wales until December 15) and for players to be able to travel between states for games, have put clubs in a tricky spot.
While most clubs haven't made public comments, the Bulldogs, who are believed to have told all their players and staff to be vaccinated by mid-September, have made their stance public in the last week.
Bulldogs' CEO Aaron Warburton told the Sydney Morning Herald that the club wouldn't have any players in their squad who couldn't fulfil contractual obligations.
"We won't have someone in our squad that can't fulfil their contractual obligations," Warburton said.
"And if they can't fulfil that, then they won't be there next year."