After making two mistakes during the Champions League final with Real Madrid in 2018, Karius was sent out on a two-year loan to Besiktas.
Despite making 61 appearances during his time in Turkey, The Athletic claims that his temporary club have no intention of pushing through a £7.25m deal.
The report adds that Karius is increasingly confident of being used as backup to Alisson Becker during the next campaign.
While Adrian currently occupies that role, the Spaniard has been linked with a return to his homeland in the summer.
Karius has a contract at Anfield until 2021, leaving it likely that Liverpool will entertain bids for his signature upon his return to Merseyside. body check tags ::