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Williams has made 13 appearances this season as the Reds' senior defence has been ravaged by injury.
The 20-year-old explained he was once asked for a quick chat by Klopp - but it was only to give him some advice.
He explained to Umm per The Mirror: "I'd probably say the captain or maybe Virg [Virgil van Dijk are the most active in the WhatsApp group chat].
"Obviously [Van Dijk] has not been playing with his injury, so before every game he is wishing all the boys good luck and stuff like that.
"And the skipper [Jordan Henderson] is the one who is always replying first.
"There was one recently [from Klopp] - 'can you come and see me please.' I was scared!
"But it was just to discuss some stuff that I could do better in games, so it was nothing to be worried about. But I was nervous."
Williams' top-flight debut came back in December's 2-1 victory over Tottenham Hotspur, a game in which Joel Matip was meant to partner Fabinho.
Matip was injured in the warm-up and it saw Williams handed a shock start.
Recalling the events, he continued: "I was nervous because I wasn't starting at first, I was on the bench. And then Joel Matip was meant to play.
"He had a problem with his back, so the boss and the first-team coach come to me and said 'be ready because you are starting, Joel has failed his fitness test.'
"So that was say five or six hours before training and I had to get my head together because that was my first game in the Premier League with [Harry] Kane and [Heung-min] Son up top.
"I was nervous but the boys helped me through it."
Injury to van Dijk, Matip and Joe Gomez has seen Fabinho and captain Jordan Henderson fill in at the heart of defence this season.
But Fabinho and Henderson have also suffered from injury and it saw the reigning Premier League champions act in January.
Ozan Kabak arrived on loan from Schalke and Ben Davies joined from Championshp side Preston North End.
Nathaniel Phillips has also played, meaning Liverpool have used 18 different partnerships so far in 2020/2021.
Liverpool currently sit eighth in the table and travel to Wolverhampton Wanderers on Monday evening.
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