The German giants want to earn around £ 35 million for the Spanish, but Liverpool only want to spend £ 18 million.
Liverpool, however, have some bargaining power, as Thiago is out of contract at Bayern Munich in the summer of 2021.
This means that the Spaniard could in theory allow his contract to end before leaving the free club at the end of next season.
Thiago is said to be keen to move to Liverpool and has put his house up for sale in Germany as a sign of his intention to leave the country.
It is understood that he also recently snubbed a new contract at Bayern.
According to the German publication Bild, Klopp also wants to get a transfer for the midfielder in the coming months.
The report says that Klopp has made an internal request to senior officials in Liverpool to make the signing of Thiago a priority.
The request was compared to a similar request made by Pep Guardiola when he was at Bayern Munich and, interestingly, very eager to sign Thiago for them.
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