The Reds have been regularly lined with a move for the midfielder this summer as Jurgen Klopp looks to strengthen his Premier League winning squad.
Bayern boss Hansi Flick has publicly stated that Thiago wants to leave, as has CEO Karl-Heinz Rummenigge, who said: "Regarding Thiago, it's known that he told us he wanted to do something new.
"If a club approaches us that is willing to pay a fair transfer fee, we will work on it."
But the player himself, who is currently on international duty with Spain, has denied those claims.
"I have not told anyone that I'm leaving," declared the playmaker on Saturday. “Every year you put me at a different club.
“For me, my future is tomorrow's game and there is nothing more to say. I neither care nor am I interested. What interests me is tomorrow."
It comes after Thiago had told ZDF on Thursday night: "Bayern is my home and I am happy to be there."
Liverpool icon Jamie Redknapp believes Thiago would be a good signing for Klopp, saying: "We've often spoken about how good Liverpool's midfield are, how hard-working they are, but sometimes they maybe lack that bit of finesse and that little bit of quality.
"Thiago would give them something completely different, he's one of the best midfield players in the world. He dictates the play, plays at his own pace.
Get the latest transfer news straight into your inbox!
Want to be on the ball with Jadon Sancho to Manchester United updates? Or perhaps you're a Chelsea fan wondering who on earth could join next?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
"Sometimes, especially when you go to tough places in the Premier League, you cannot beat teams by going 100 mph all the time, you need a little bit of finesse and for someone to do things differently.
"Many years ago Liverpool had midfield players like Ronnie Whelan and Jan Molby who could just slow the game down and play at a tempo that suited them, Thiago could do that.
"We saw him in the Champions League final where he completely bossed the game, had so many touches of the ball and made the game look easy."