The 30-year-old missed most of last season following a serious tackle by Everton goalkeeper Jordan Pickford in October, only one of various fitness gives the Reds experienced last season.
Van Dijk, Joe Gomez (knee), Joel Matip (lower leg) and Trent Alexander-Arnold (thigh) are altogether dealing with their fitness and has participated in Liverpool's pre-season preparation in Salzburg, Austria.
"Every one of the four look great, I need to say," Klopp told the club site.
"Van Dijk and Joe won't have twofold meetings now for the initial not many days with the team ... I don't know precisely when we can make the following stages however it will occur in the following month, without a doubt we will get a big step forward.
A 'wonder' if Virgil van Dijk plays again for Liverpool this season, says Jurgen Klopp
"Joel looks great, totally, he is the nearest presumably to typical preparation... Trent was a genuine physical issue however presently not a significant one, I would say. He is close however at this time, likely the following five or six days he will be available."
Liverpool, who completed third last season, start their new match with newly promoted Norwich City on August 14.
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