Simon Mignolet has held the position for a number of years, but Klopp has continued to involve Karius since his arrival ahead of the start of last season.
Karius started in the 4-3 victory over Manchester City last weekend and although the German stopper could have potentially kept out City's opener, Klopp has said that he will start against Swansea City on Monday night.
At a press conference, the 50-year-old said: "I was always very positive about Simon [Mignolet]. It's difficult to be a goalkeeper or central defender at Liverpool. I am fine with our goalkeeper situation.
"Yes, Karius could have saved 1st goal versus City but he's a really good goalkeeper. He has settled, a lot of things about his game are natural. Loris needs to deliver and he knows that. He's the number one now."
Karius has made 27 appearances during his first 18 months on Merseyside.