The Reds goalkeeper terminated his loan deal with Besiktas this week citing unpaid wages as reason.
The Liverpool Echo says senior figures at Anfield are unhappy with how their player has been treated in the Turkish capital.
As things stand now, though, his season is over, with Liverpool unable to register him for the return of Premier League football.
Even when Melwood re-opens its doors, it is unclear if a decision will be taken to permit Karius to train with his parent club once more.
The preference, it is believed, is to give him an extended break and to find a permanent buyer for the 26-year-old.