With Jordan Henderson injured and James Milner returning from a hamstring problem, Klopp asked his players to select a new skipper and vice-captain for the Champions League clash.
Van Dijk, 27, was picked to wear the armband, while his Netherlands team-mate Georginio Wijnaldum was second.
"I really think Milly and Hendo are doing an outstanding job for the club and the team. Being ambassador for the club on one side and impressive for the team on the other side is brilliant. They combine pretty much everything," he told UK newspapers.
"When I came in I built a players' committee. There were five, six players including Lucas Leiva, Adam Lallana and Phil Coutinho. This team has grown now and they all have very, very demanding and confident players in the squad so you can decide who of them you want.
"It was a close decision. Dejan [Lovren] was close, Adam was close. They all had their votes. The players see it in the right way – that the players could do the job.
"Virgil is still young. He looks more of a man than he really is. There is nothing wrong with that and he can still improve. If you see and hear him, you think there is a big distance between him and you because he looks quite impressive.
"It is good for him to have this responsibility and there will be a day for sure when Gini will wear the armband. He will be very proud of that as well."
Liverpool are unbeaten in the Premier League this season and sit second to Manchester City on goal difference.