Thiago, 29, joined the German giants from Barcelona in 2013 and played in last season’s Champions League final victory over Paris St-Germain.
Talks are ongoing between Liverpool and Bayern over the player, who has one year left on his contract.
Thiago would be the Premier League champions’ second summer signing, after Greece left-back Kostas Tsimika.
When asked about a potential move for Thiago last week, Liverpool manager Jurgen Klopp said: “I cannot end speculation as long as the transfer window is open. Did I mention that Thiago Alcantara is a really good player? Long time ago.
“It is nice that we are linked with him but that is pretty much it really. It is because he is a good player and Liverpool is a big club, so that is nice.”
Thiago started his career at Barcelona and was heavily linked with a move to Manchester United when David Moyes replaced Sir Alex Ferguson in 2013, but the move did not transpire and he went to the Germany instead.
As well as the Champions League, he has won seven consecutive Bundesliga titles, four German Cups and the Club World Cup with Bayern.