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Having previously taken in a relatively quiet window, the reigning Premier League champions are starting to splash the cash.
Thiago has been acquired from Bayern Munich, while £45 million ($58m) has been invested in former Wolves star Diogo Jota.
The latter is yet to make his bow for the Reds, but one new recruit was let off the leash during a 2-0 victory over Chelsea at Stamford Bridge.
The 29-year-old’s passing ability was on full display in west London, with Mane telling Sky Sports afterwards: “Not only me, all the world knows what he is capable of doing.
“He is one of the best players in the world, so we are lucky to have Thiago in our team. And I think he showed that he is a great player.”
Klopp’s side controlled proceedings throughout against Chelsea, with Thiago replacing Jordan Henderson at the interval after the Reds skipper picked up a slight knock.
Mane added: “Obviously it was a top game, to be honest.
“It was a top game. Especially in the first half, we found it very difficult to create chances and I think when they got the red card, it made it easier.
“The second half, we created many chances and finally we scored two goals. I think today we deserved to win.”
Liverpool’s cause was aided considerably when Andreas Christensen was dismissed late in the first half, with a VAR review leading to an initial yellow card for the Danish defender being turned into a red.
Mane was at the centre of that incident, with the Senegalese forward hauled down as he raced through on goal, before going on to head home the opening goal and make Kepa Arrizabalaga pay for another moment of madness.
He said of chasing down the under-fire Chelsea goalkeeper and blocking his clearance after initially giving the ball away: “Yeah, sure, these kinds of things are always what we try on the training pitch.
“When he got the ball, I knew it will be difficult for him to have an option, the only choice was to shoot it.