Van Dijk collided with Moussa Sissoko while successfully defending a two-on-one Spurs counter-attack in the 85th minute of Sunday’s match at Anfield.
The Reds went on to win the game in dramatic circumstances, courtesy of Toby Alderweireld’s last-minute own goal at the Kop end.
When asked about Van Dijk’s condition during his post-match press conference, Klopp replied: “We have to see. I asked him and I think it was in the counter-attack situation when Sissoko hit him… I don’t know if he twisted it or it is a knock.
“He was walking to the interviews with a big ice pack. I hope it’s nothing serious but I don’t know yet.”