Barca are keen on re-signing the midfielder, who left the Nou Camp for the Bundesliga giants in 2013, while the Reds have been strongly linked with a move.
New Barcelona boss Ronald Koeman is reportedly looking for a midfielder this summer with Liverpool star Georginio Wijnaldum also on the radar.
Ivan Rakitic has already left Barcelona with Arturo Vidal potentially following him out of the Nou Camp exit.
Though Mundo Deportivo claim that Barca believe a deal for Thiago would be complicated as Liverpool are in advanced stages over a transfer to sign the Spaniard.
Bayern boss Hansi Flick had publicly stated that Thiago wants to leave, as had 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."
Liverpool icon Jamie Redknapp believes Thiago would be a good signing for Jurgen 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.
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"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."