Thiago has been heavily linked with a move to Anfield during this transfer window with reports previously suggesting personal terms had been agreed.
Jurgen Klopp is believed to be eager to improve his options at Liverpool despite guiding the Reds to their maiden Premier League title this season.
But reports in France suggest their pursuit of Thiago won’t be easy, with competition for the midfielder.
That offer will match what Bayern are asking for, potentially leaving Liverpool wondering what to do next.
Liverpool are unexpected to spend heavily this summer, though Klopp said: “I have no idea who will play for me next year, there is nothing to say at the moment.
“Thiago Alcantara is a great player, but also a Bayern Munich player. That’s actually all there is to say. There’s nothing to say!”
Liverpool icon Didi Hamann recently urged Klopp to sign Thiago to upgrade his “workhorse” midfield.
“He doesn’t quite fit the profile of the Reds’ transfer policy at his age,” Hamann said. “Regardless, a transfer would make sense in my eyes.
“Jurgen Klopp has more workhorses in his midfield with Jordan Henderson, Fabinho and Naby Keita. He could use an intricate technical player like Thiago well.
“On the other hand, he will surely have a new contract at Bayern waiting to be signed. I would be surprised if he was not offered a lot to stay.”
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Though another former Liverpool player has questioned where Thiago would fit at Anfield with Luis Garcia saying: "If top players come to Liverpool and you have to move one of the ones that are moving at the moment, that's not easy.
"If you see [Naby] Keita, the way that Keita plays is similar to Thiago. The way they move, the place that they play is very similar.
"Keita is still adapting to the Premier League, are you going to move him from that place?"