Thiago has entered the last 12 months of his contract meaning Bayern risk losing him for free next year.
To avoid that situation, the Bundesliga side may have to sell the 29-year-old for a cut-price fee of around £30million.
BILD's head of sport Christian Falk has detailed how close Thiago is to moving to Anfield.
"I think he will leave but he has to bring a club. He is very sure that he has a club and we know the club.
"But the big question is is the club paying the fee that Bayern Munich is expecting.
"We are talking about Liverpool. They don't want to spend so much money this year and we know why they missed [Timo] Werner.
"If a player like Thiago is on the market, and they need a player in this position, then it is a question of money.
"They don't want to let him go for free next summer."