Van Dijk could make his debut in the FA Cup tie against Everton next Friday but Klopp reiterated that he won't rush the 6ft 4ins defender into action for the Reds.
He intends to assess him at Melwood next week before deciding when to draft him in.
"I don't know how much time he will need because we play differently from Southampton," Klopp said.
"We don't have a lot of time to train but okay between the Everton and Man City games there is a little bit more time.
"There are so many things he still needs to work on but he's at a wonderful age. He's developed a lot in the last few years and made big steps so it is a good thing.
"It's a long-term project and I don't feel any rush with him. If he is 100% we can use him.
"If not we'll bring him to 100% and then he will be ready."