Van Dijk has started all 23 league games for the Reds this season, winning December's Premier League player of the month award, but has been struggling with illness ahead of Wednesday's visit of the Foxes.
Former Southampton and Celtic centre-back Van Dijk has played a key role in Liverpool's stunning campaign, with Klopp's side four points clear of last term's champions Manchester City.
He has been nursing a virus over recent days and would be a big miss if forced to sit things out in midweek.
Liverpool have major problems in defence for the Leicester game without bringing Van Dijk into the equation, with Joe Gomez still recovering from a fractured leg while Trent Alexander-Arnold has a knee injury.
James Milner filled in at right-back in Liverpool's last Premier League game, a 4-3 win over Crystal Palace at Anfield, but he is suspended as he was sent off late in that game, with another makeshift option - Fabinho - another of those to have been nursing a knock.
However, Dejan Lovren could come in as the Croatia defender has been passed fit following a hamstring injury.
"Virgil was a little ill but he trained yesterday [Monday], so we will see. He will train today, so we will see," Klopp told reporters.
“Gini trained, Fabinho will train today, Trent is getting closer and closer and it looks all very positive, but he will not be ready for tomorrow. Joe is a no.”
With Liverpool having been knocked out of the FA Cup, Klopp took advantage of a rare break in his side's schedule to take his squad to Dubai for a warm-weather break.
"It was good we could do that and usually you'd say no games in that time, usually one game in that time would be good, difficult lineup-wise as we needed couple days for the boys and a few players were not a part of training until a few days ago," he added.
"But it was good, we didn't have to play important cup competitions but it would not have been possible for a lot of players. We had a few more days and now have to show [it made a difference]. But Leicester are in the same situation so it's not a massive advantage.
"It's just the situation and they can bring back [Harry] Maguire I heard after injury in the last game and so we had a few more days and could wait for one or two players but we have to see if they are available for the game."