The Reds have long been linked with a move for Thiago, who is in the final year of his contract at Bayern and has expressed his desire to leave in pursuit of a new challenge.
Earlier in the summer it was claimed that personal terms had already been agreed with the 29-year-old, but there had been no progress with regards to a deal with the Bundesliga champions.
But now, the Merseyside press have confirmed that the Reds are pushing ahead with a move regardless of any further sales.
The Athletic‘s Simon Hughes ran an exclusive reporting that a deal worth around £27 million was close, with this soon followed up by the Times‘ Paul Joyce and the Evening Standard‘s David Lynch, among others.
Lynch writes that the deal is “picking up pace,” with the Mail‘s Dom King describing this as the club’s “first move” for the Spain international.
Speaking last week, Jurgen Klopp said: “I cannot end speculation as long as the transfer window is open, so that’s all I can really say about that.
“Did I mention that Thiago Alcantara is a really good player? [I did] long ago already!
“It’s nice that we are linked with him, but that’s pretty much all, really. It’s because he’s a good player, Liverpool’s a big club, so that’s nice.
“But apart from that, really nothing to say about that. And maybe good for you, I cannot end the speculation!”
“He’s the player of the league, that’s how it is,” he said of Keita. “Last year together with Thiago Alcantara, who played outstanding for Bayern, he was the flier.”