The Reds have ramped up their efforts to land the Bayern Munich star after the German club put a deadline on a bid.
With the Bundesliga season readying itself up to start, the champions wanted all their business concluded by that date.
It saw Liverpool submit a £20m offer, with £5m in bonuses, which was accepted.
Thiago has always maintained that he would like to move to Anfield this summer to try on a different challenge.
And he looks set to get his wish, while personal terms should not be too much of a problem.
But with Liverpool facing Chelsea on Sunday, it remains to be seen whether or not he will officially join before that date.
They will have until midday on Friday to submit all the relevant paperwork or he will not be allowed to play against the Blues.
It means Jurgen Klopp faces a race against time if he wants the midfielder to take part.
But, in all truth, the German manager will most likely prefer if his prospective new signing does not feature.
The 53-year-old favours a system that carefully and slowly introduces new members of the squad to the first-team.
It is the same treatment he gave to the likes of Takumi Minamino and Fabinho, and it means even Liverpool's next game might not feature Thiago.
While this weekend's clash comes on Sunday, the Reds are next in action against Lincoln on Thursday.
Klopp has cared little for the Carabao Cup during his time at Anfield and with a season full of fixtures, that could continue.
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It means Thiago may have wait a little longer for his debut.
The Premier League champions face Arsenal after their clash with the Imps, who are flying high under Mikel Arteta.
The Reds kicked off their defence of the title with a high-octane 4-3 win over Leeds United.