Last weekend, Van Dijk marked his first appearance since a £75m move from Southampton with the winning goal as Liverpool defeated Everton in the FA Cup third round.
However, Klopp has suggested that he may leave the Netherlands international out of the team for the visit of the league leaders on Sunday afternoon.
The 50-year-old told reporters: "The Everton game showed he can adapt to the job. He was impressive, we have to say that. I wasn't sure before the game but I was very sure afterwards.
"The City game is a completely different game and the tactics must be as tuned as possible. I haven't decided if he is ready."
City had been heavily linked with a move for Van Dijk before Liverpool were able to push through a deal for the 26-year-old.