The defender picked up a knock in the second half of the Premier League clash at Anfield over the weekend and he was replaced by Joe Gomez in the 55th minute on Merseyside.
Liverpool FC are next in action in the third round of the League Cup against Chelsea FC at Anfield on Wednesday night, and it remains to be seen whether Van Dijk will be ready for that game.
However, Klopp has played down the injury concerns surrounding Van Dijk and says that the problem should not be a serious one for the Netherlands defender.
Speaking at his post-match news conference, Klopp said: “He already had a bruise in the ribs before the PSG game, which is very uncomfortable and today he got another hit there.
“It’s not cool but should not be too serious.
“It should be absolutely OK, hopefully. I didn’t hear anything different.”
Liverpool FC have won all six of their opening six Premier League games this season to make a 100 per cent start to the new campaign.
The Reds are aiming to try and challenge for the Premier League title this season after they finished in second place last term and without a trophy under Klopp.
They reached the Champions League final but ended up losing to Real Madrid back in May after a 3-1 loss in Kiev in the showpiece.
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