Klopp says he wants Karius and Mignolet to be pals, even though they are now direct rivals.
"I knew when we signed Karius that we now have two really strong goalkeepers," said the Reds boss.
"That was the plan, but unfortunately Loris broke the bone in his hand, which is not too cool for a goalkeeper.
"But he is now back. There is no pressure or anything like that. It is about the challenge and the competition.
"In the end, I want us all to be best friends, even when our best friends play in the same position.
"That's how it is, that's football, it's about performing. And we all have this pressure. I'm happy that Loris is back. He's a great, great character - a really good guy - and a real goalkeeper so that's good.
"I'm fine and if they all stay fit in this position, that's all I need."