I think the wheels behind the rumour are maybe the quotes from Klopp in 2017 and 2019.
https://www.liverpoolfc.com/news/first-team/274605-klopp-i-got-so-many-congratulations-when-we-announced-keita-deal “I have contact to a lot of people in the Bundesliga, as you can imagine, and I have never had so many congratulations messages as I had after signing Naby!
“He's the player of the league, that's how it is. Last year, together with Thiago Alcantara who played an outstanding season for Bayern, he was the flier. He's been doing this for two or three years, with different clubs in different leagues, but he's still a young boy.”
Then after the 0-0 at Anfield last year.
“Kimmich and Alaba were so disciplined tonight. I've probably never seen them defend like that. Respect to them they made it difficult for us, although we had good situations where we missed the last touch.
Thiago is a world class footballer. He played that deep-lying playmaker role very well. Alongside Martínez, they were very good.”
Who knows. Jürgen certainly likes the player.