The goalkeeper has been in poor form for Liverpool in recent weeks.
Karius joined the Reds in the summer transfer window as Klopp sought out a replacement for Simon Mignolet.
After missing the start of the season with an injury, Karius has established himself as number one over the last few months.
He is so far yet to impress, though, with many still unsure whether he is good enough to be Liverpool’s long-term number one.
The last two weeks have been particularly rough, with a mistake against Bournemouth and then failure to keep out a Dimitri Payet free kick on Sunday earning him strong criticism.
Carragher is one who has been less than impressed and claims the German is currently killing Liverpool.
“Jurgen Klopp may feel that's [dropping] going to kill the lad's confidence but at this moment he's killing the team on the pitch,” he told Sky Sports.
“Liverpool should probably have another six points. They are probably five points down on what they should really have.”
The pressure is definitely on Klopp to make a decision about his current number one.
Karius has not been performing for several weeks and as Carragher points out, that is already costing Liverpool in the title race.
With Chelsea in fine form and now six points clear the Reds cannot afford to keep dropping points by standing by their man if he continues to under-perform.
It is a big decision for Klopp to make and it will be interesting to see what he does, especially in this crucial stage of the season.