Reports soon leaked that Thiago will sign a four-year deal at Anfield once the transfer formalities can be finalised and the player completes a medical.
Although no confirmation of the move has been made, Bayern coach Hansi Flick has revealed that Thiago has already bid farewell.
“Thiago is an exceptional player who spent seven hugely successful years here," the Bayern boss said.
“He's a wonderful person and an outstanding professional.
"It was very emotional today when he said goodbye to us all. My coaching team and I enjoyed working with him. I can only congratulate Liverpool as they got a great player and especially a great person.”
Bayern ultimately decided to cash in on the Spain international as he has now entered the final year of his contract.
They are involved in a similar quandary with David Alaba, but are hopeful that the Austrian will sign a new deal in the coming weeks despite a high-profile spat between the player's agent and Bayern CEO Uli Hoeness.