Liverpool extended their lead at the top of the table to 10 points after beating Watford 2-0 on Saturday, with Gomez and Van Dijk helping them keep back-to-back Premier League clean sheets for the first time this season.
Gomez has only recently returned to a regular starting role due to injuries to Dejan Lovren and Joel Matip, Liverpool's two other recognised centre-backs, and Klopp is pleased with his impact.
"These two, Joe and Virg, they like each other a lot, and can play sensationally well together," Klopp said.
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"This outstanding skilled boy (Gomez) ... hasn't played consistently for a while. He has improved a lot."
Gomez and Dutch international Van Dijk formed a formidable partnership last season before the Englishman was ruled out of the second half of the campaign with a broken leg.
The 22-year-old has started only three Premier League games this season, but Liverpool have kept clean sheets in two of those - their consecutive league wins over Bournemouth and Watford - taking their total for the season to four.
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"In a very good team ... the train doesn't wait," Klopp added. "That means other players showed up (when Gomez was injured).
"The boy is still young, that is not the reason (why he has not played regularly) - it's just that you keep rhythm and you keep players together."
Liverpool are next in action against Aston Villa in the League Cup on Tuesday and play Mexican side Monterrey in the semi-finals of the Club World Cup in Qatar on Wednesday.
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