The ex-Reds defender revealed that in 2017, there was a boiling tension behind the scene as the boss and the midfielder were ready to fight.
once wanted to get into a fight, according to
, with the Reds manager ready to have "gone all the way just to prove his point".
In 2017, after a 2-2 draw at Sunderland that was keeping them more behind from reaching the title, there came a lot of pressure at Anfield.
The German tactician and the England international squared up in the dressing room but the latter backed down.
The centre-half, who played for Liverpool from 2016 to 2018, told the Betsafe Eesti Podcast: "
The biggest pressure was around Christmas and at the beginning of January. One time, I don't remember who we played against. Maybe it was against Sunderland away.
"Klopp and James Milner almost started a physical fight. It was the period when there was Boxing Day in England and they almost started fighting but eventually Milner stepped back.
"We saw from his eyes that Klopp would have gone all the way just to prove his point. It was the most stressful time for him as well. He was under a lot of pressure.
"It was my first and Klopp's second year. What are you going to do? You're supposed to be a good coach. You are Jurgen Klopp who will make superstars of all players. The pressure started getting to him.
"It's not supposed to be easy, but if you don't deliver against a team like Sunderland, then you can forget about the places you had hoped for."
The 2016-17 campaign had the Reds finish in fourth, but in the years after, they claimed the Champions League crown as well as the Premier League title.
The success was not a surprise to Klavan, as Klopp is one of the best coaches that he has worked with.
He went on to talk about the German’s man-management skills and ability to deliver results:
"What I didn't have with other coaches in team meetings is he never repeated himself. He always talked from a different angle or there was a slight joke in it.
"He sensed the player and the team so well. He knew when to say what. If he saw there were problems in the team, he could turn it around with a simple joke or vice versa, when the team didn't take it too seriously, then he showed them who's boss. That, for me, is his phenomenon. That he can read the team so well, and individually as well."
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