Munich crushed Barcelona 8-2 with Thiago in the team on Friday, but the Spaniard has turned down the chance to discuss a new contract with the German giants and wants to join Liverpool.
He is out of contract at the Allianz Arena next summer and Liverpool are reluctant to meet Bayern Munich’s asking price.
Talks are set to take place between the two clubs, but according to German daily Bild, they will only commence following the Champions League.
Liverpool have put the brakes on their spending in recent years and it remains to be seen if they will be able to reach an agreement to land Thiago.
It has been claimed in some quarters that Thiago already has an agreement on personal terms with Liverpool.
He is keen to play under Jurgen Klopp at Anfield as he looks to sample Premier League football with the current champions.
Thiago, 29, has made a total of 233 appearances for Bayern Munich since he completed a move to the club from Barcelona in 2013.
