Liverpool signed the Dutchman for a club record £75m this week.
Klopp had wanted to sign Van Dijk last summer but those hopes were dashed when Liverpool stood accused of making an illegal approach and ended up issuing an apology to Saints.
At the time the Reds boss was heavily criticised for not pursuing an alternative centre-back target.
Asked if that was because he was always confident he would get Van Dijk in January, Klopp said: "I will not say anything about that because I am still not sure what I am allowed to say about last summer without my lawyer!
"The first time I saw Virgil he was playing for Celtic. But it was only during his time at Southampton really that I saw enough games of him. When he was still in Holland I did not think about him too much."