Klopp revealed in his press conference after the FA Cup final that he told Thiago, 'If I would have known what a player you are, I would have signed you four years earlier.'
The midfielder responded to him by claiming the Reds boss had taught him 'running' in his two seasons on Merseyside.
"We're a pair that love jokes," Thiago said, explaining the conversation. "It was a very charismatic and humble moment between us both and we were very happy with the FA Cup that we achieved.
"We were talking about the good stuff that we learned, just having fun but serious at the same point. It was about the style of team that he created.
"We have to chase the ball, open up all the field. I was in a couple of teams where we love to dominate the game, we have to be in the other team's half of the field.
"Now we have to chase them over, so you have to learn that and how to behave in all the situations. It was a great experience as well."
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