According to Fi's news, Liverpool accepted the lease offer for Karius from the Berlin Union.
Karius has been allowed to undergo a joint medical examination in Berlin on Monday, local time, and he hopes to return to the Bundesliga to find his status.
Liverpool coach Klopp told Karius earlier in the summer transfer window that he could find his next home.
Liverpool had hoped to sell Carrius directly, and the players have been loaned to Besiktas in the past two seasons.
Besiktas did not choose to activate the £7 million buyout clause. Liverpool had hoped to recover the cost price of £4.5 million.
Now Karius is allowed to leave again on loan to help Liverpool reduce salary expenses.
Klopp did not intend to return Karius to the lineup this season, and now the player will return to the Bundesliga.