Goal report that the Merseyside club are now looking to reward the player after his successful loan spell at Hull, which saw him score seven goals in 14 appearances for the Yorkshire side, with a new contract.
However, Karius proved he was desperate to remain in Klopp's plans as he appeared in the Reds' opening pre-season friendly against Chester FC on Saturday.
"After four days I got a call from Franz Beckenbauer, [Germany's] Bobby Moore, our biggest football player who is a good friend of mine", Klopp told the club's official website.
On his aims for the season ahead, he added: "I think my short-term focus is to keep trying to impress the manager day in, day out in training and, the minutes I get in pre-season, try and impress".
Did you manage to pick up much of a tan at the cricket yesterday? We don't think about that anymore and we start completely new.
I can see Wilson doing a Kane, where he goes on loan after loan and eventually shows his worth in the league! Woodburn out on loan??
"I'm a lot of things but not blind, so that means I see what they offer - and if someone offers something special then I will realise it and we will make decisions about it".
Worth keeping, hows Woodburn doing??