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The 29-year-old, who has made 35 appearances in all competitions for the Bundesliga side this season, scoring three times, has already held talks with Bayern over a new contract, with his current deal due to expire in 2021.
But despite both parties being close to reaching an agreement, the Spanish international had second thoughts about penning a new contract and appeared to fancy a new challenge.
In fact, according to SPORT, a deal is 'very close' between the two clubs and the signing could be finalised soon.
If a deal materialises, Liverpool will certainly have a player on their hands.
Thiago has spent seven trophy-filled seasons in the Bundesliga with Bayern after previously enjoying eight years with Barcelona and in that time, he has established himself as one of the best centre-midfielders in world football.
Jurgen Klopp has never been one to shy away from the fact that he admires Alcantara's talents.
He spoke fondly about the player after Liverpool's clash against Bayern Munich in the Champions League last season.
"I've probably never seen them defend like that," he said. "Respect to them as they made it difficult for us, although we had good situations where we missed the last touch.
"Thiago is a world-class footballer. He played that deep-lying playmaker role very well. Alongside [Javi] Martinez, they were very good."
If you are unaware of Thiago's talents, then just take a look at his outrageous pass against Hamburg that did the rounds again last month.
The Spaniard cuts across the ball on the half volley, sending Franck Ribery through down the left with the most satisfying pass. The slow motion replays give this pass another dimension.
Thiago Alcântara that is disgusting pic.twitter.com/xLGOX0eDxD
- Hunter Godson (@HunterGodson) June 22, 2020
Are Liverpool fans happy with the possible addition of Thiago?
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