Meanwhile, Philippe Coutinho (thigh) and Mohamed Salah (groin) both remain sidelined for the FA Cup third-round tie at Anfield.
However, speaking at Thursday's pre-match press conference, Klopp insisted he will field the 'strongest line-up' available to him in what will be the 230th Merseyside derby.
The Reds' starting XI will include Karius, with Danny Ward set to be named on the bench. Van Dijk's involvement is not certain, though.
The centre-back is available to represent the Reds for the first time following his January 1 transfer from Southampton after training with his new teammates at Melwood this week.
But Klopp stressed he is keen not to throw his new No.4 into match action too soon, saying: "He is healthy and now I have a decision to make for this game. It is not finally done, so we will see what we do with him.
"As I have said before, from our point of view there is no rush for us in this situation and it's much more important how many good games he can play for us than how many and when it starts."
From an Everton perspective, Sam Allardyce revealed on Thursday that defender Michael Keane is the visitors' only fresh injury doubt.
"He had five or six stitches on the crown of his foot after the Manchester United game and it would probably be too much of a risk, but everyone else is OK," the Blues' boss explained.