Thiago arrived to huge fanfare when he completed his move from Bayern Munich in September, but has found his game time heavily restricted by injury so far.
The Spaniard returned to action over the Christmas period, and it has coincided with Liverpool going three games without a goal and seeing their title defence fizzle out.
Hamann, who was at Anfield from 1999 until 2006, believes that the 29-year-old, though a fine player, does not suit Klopp's set up and is slowing them down.
He tweeted: "Liverpool had a lot of possession for quite some time now and always found a way to break up defences.
"The dynamics of the team will change with Thiago in the team. I don't think for the better
"He's best when the team got long phases of possession, everything Liverpool of the last few years is not."
Hamann was justifying himself after he appeared on talkSPORT on Tuesday, and urged caution over whether Thiago will be able to turn around Liverpool's fortunes amid their poor run of form.
"He slows things down and doesn't really play the way Liverpool play," he said.
"Liverpool in the past have had hard-working midfielders, they were not as skilful as Thiago, but they have the ball to Mane and Salah early.
"If you get the ball early on the wing, and theses guys can run at players they are very hard to stop.
"I just feel with Thiago, everyone was raving about him coming to Liverpool, he's hardly played. He came on against Chelsea and had the most passes in the second half, against a Chelsea team that was down to 10 men.
"He came on against Newcastle in the last 25 minutes, Newcastle were dead on their feet, everyone was raving about how good he is.
"I can tell you, he's a good player, a skilful player. But there was never a time in Munich where people said, 'oh he's the first on the teamsheet'. So I'd be very cautious when it comes to Thiago.
"And the other thing is, as other people alluded to earlier, he plays a different style of football. He likes to be in possession.
"Liverpool were always good when they weren't in possession, won it and played quickly forward.
"He's not that type of player, so it will be very interesting when he does play more often now how it's going to change the dynamics of the team."