Other sources believe the final fee will be closer to €30m (£27.5m) for Thiago, who is in the last year of his Bayern contract.
Thiago, 29, will sign a four-year deal with Liverpool and wear the number 6 shirt.
Liverpool have been pursuing the Spain midfielder since June, but an agreement with Bayern was not quick.
Liverpool planned to sell a midfielder before bringing in Thiago, but with nothing imminent stepped up talks.
Jurgen Klopp believes Thiago can add an extra dimension to the Liverpool midfield with his versatility.
Thiago’s passing and ball retention ability will mean Liverpool are better equipped to control matches.
He will leave Bayern after seven trophy-laden seasons which included nine Bundesliga titles and the Champions League.
Bayern coach Hansi Flick commented on the departing Spaniard.
“We are very sad, the goodbye this morning was very emotional,” Flick told the German press. “Congratulations to Jurgen Klopp, he gets a top player and a top person!”