The Spain international has made it clear he will not be signing a new contract at the Allianz Arena with his current deal expiring next summer.
Bayern would rather let him go than lose him for nothing and have an asking price worth around £27m.
He joined Bayern in 2013 but after seven years is keen on a new challenge with club chiefs happy to sell.
Liverpool have emerged as the ideal destination with both club and player keen on a move.
However, the Reds are yet to meet Bayern's asking price and are determined to bring it down.
The Premier League champions have made just one signing this summer, Kostas Tsimikas, who will act as back-up to Andy Robertson.
And Liverpool legend Graeme Souness has been disappointed by his former club's work in the transfer window.
"The perfect time to sign players is when they do not have to be an instant hit but can be gradually introduced," Souness wrote in The Times.
"So I am disappointed that Liverpool haven’t done so while they are reigning Premier League and world champions.
"That worked well with the likes of Fabinho and Robertson, who came to the fore after spending several months learning the system and could bed in without the spotlight being on them."
The Scotsman went on to insist that he beleieved that this year is the perfect time to snap up Thiago.
He added: "Thiago Alcantara, the Bayern Munich midfielder, would be perfect because he works his socks off but is also gifted technically.
"He is 29, but he still has a couple of years, maybe three, at the highest level left in him."
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Nevertheless, he has still enjoyed huge success since joining the German giants, spending the last seven years in Bavaria.
In 231 appearances, he has scored 31 goals and has won seven Bundesliga titles as well as four cups.