The Reds have been heavily linked with a move for Thiago, with reports from around Europe claiming Liverpool have gone as far as to agreeing to personal terms with the 29-year-old.
However, despite persistent reports from abroad, Liverpool have seemingly informed local journalists that the transfer is simply a "fantasy." The Echo have even gone on the record four times to state Thiago is not being considered by the Reds.
But there's mounting talk of the deal going ahead, with the club perhaps trying to keep a lid on their business - learning from past mistakes in the transfer window.
Along with journalists Fabrizio Romano and Christian Falk, the Independent's Melissa Reddy has stated Liverpool have made advances for the midfielder.
Ahead of Bayern's Champions League final win over PSG on Sunday, Romano once again reiterated Thiago would be playing his last game for the Bundesliga champions. He confirmed Thiago has his mind set on playing for Jurgen Klopp, with only a transfer fee left to agree.
It adds to a report from one of the few English sources during the transfer saga so far, with journalist Kevin Palmer claiming before the final that a source has told him a deal "will be done."
"Thiago will aim to collect his second Champions League winners' medal and will then tell Bayern chiefs that he wants to move to Liverpool, who have already made tentative steps to sign him," Palmer wrote.
"While Thiago and his advisers have made no secret of his desire to link up with Jurgen Klopp's Premier League champions, Liverpool insiders have persistently insisted they are not interested in signing the player.
He later added to his report, tweeting: "Deal will be done... if Wijnaldum leaves." When asked how likely the Dutchman was to depart Anfield, he replied: "Very possible at this moment. We’ll find out soon enough."
Palmer was the first journalist to break Liverpool's interest in now Reds defender Virgil van Dijk and, should he be correct, the Reds may be bracing for Wijnaldum to leave the club this summer - or in January.
Wijnaldum doesn't appear to be any closer to signing a new contract extension, despite now entering the final 12 months of his current deal. The confirmation of fellow countryman Ronald Koeman as new Barca manager has supposedly sparked his interest.
While a departure this summer remains unlikely, should Liverpool secure Thiago, it may make the club consider receiving a transfer fee for him now, rather than allowing him to leave for free next year.
With most reports up to now claiming formal talks between Liverpool and Bayern for Thiago won't begin until after the Champions League final, we should find out more about this saga in the coming days - one way or the other.