The Dutchman missed the Carabao Cup defeat to the Blues in midweek after nursing a rib injury picked up before the PSG clash last week.
Liverpool fans were hopeful Van Dijk would be fit enough to return alongside Joel Matip at Stamford Bridge tomorrow evening.
However, in his pre-match press conference this morning, Klopp hinted that the £75m signing won’t win his race against time to face Chelsea.
“Virgil is a world-class player, and if you miss a world-class player always it’s not cool,” he told reporters.
“But [Dejan] Lovren played his first game in 10 weeks.
“He played an outstanding game.
“Matip, two games in a row, fantastic.”
“If Virgil is fit, he plays. If not, then obviously we have options.
“We can play without Virgil, thank God. But I prefer if we can.
“The last game he wasn’t available, now we will see for tomorrow.”
However, Klopp did offer fans some hope, claiming Trent Alexander-Arnold and Georginio Wijnaldum were fit to return this weekend.
The former had been struck down with illness in recent days.
Liverpool’s Carabao Cup journey ended at the first hurdle at Anfield on Wednesday evening.
But Klopp went on to admit he is happy with how his side performed.
“We had 5 players with their first start of the season v Chelsea,” he added.
“It was a really difficult task. I was happy how we adapted in the game.
“We had the bigger chances but we lost it.
“We are competitive. That’s what we have to show again.
“The Chelsea game was a very interesting game.
“We needed time to adapt without the ball. It felt like things weren’t comfortable.
“It was because of little, little details. It was a big challenge for the boys.”