Last month, it was claimed that the European champions had identified the Spain international as a potential signing during this summer's transfer window, with Reds head coach Jurgen Klopp keen to boost his midfield.
Thiago has again been a key player at the Allianz Arena this season, making 35 appearances in all competitions, but the 29-year-old's contract at Bayern is due to expire next summer.
According to Sport, the midfielder 'seems set' to join the Merseyside giants, who are currently locked in 'very advanced' negotiations with both the German champions and player.
The report claims that Bayern want €35m (£31.6m) for the former Barcelona youngster, although Liverpool are not prepared to part with the full amount in a one-off payment.
Thiago has made 230 appearances for Der FCB since arriving from Camp Nou in 2013, winning seven Bundesliga titles during his time at the club. body check tags ::