Karius has not played a competitive match for the Premier League club since his two errors helped Real Madrid win the Champions League final on 26 May.

In July, Liverpool made Alisson the world's most expensive goalkeeper.

Karius, 25, travelled with the squad for Monday's league match at Crystal Palace but was not included.

If he agrees to the loan, it would leave Simon Mignolet as Liverpool's only senior back-up to Alisson, who was signed from Roma in a deal the Italian club said was worth up to £66.8m (72.5m euros).

Besiktas will have the option to buy Karius at the end of his loan.

The Istanbul-based club are 15-time Turkish Super Lig winners and are top of the table after winning their first two matches of the season.