Liverpool have been quiet in the transfer window with only Greek defender Kostas Tsimikas arriving so far.
Thiago enjoyed an outstanding season with Bayern Munich, winning the treble and playing a crucial role in central midfield.
The Spaniard has informed Bayern he will not be signing a new contract and wants to leave this summer. And the German side have put a £27million price tag on him but Liverpool are yet to submit an offer.
Klopp has decried the big-spending done by his Premier League rivals but the addition of Thiago would give his side a major boost in quality.
Speaking ahead of Liverpool’s Premier League season opener against Leeds, Klopp was asked about the speculation around Thiago.
And the Premier League manager of the year downplayed the rumours.
He said: “If I could invent a word to end speculations I’d be really rich. Did I mention that Thiago is a really good player? It’s nice that we are linked with him but pretty much that’s all.
“Good for you I cannot end the speculation.”
Meanwhile, PFA Young Player of the Year Trent Alexander-Arnold says he is confident his fitness can cope with the quick turnaround between seasons.
“Yeah, it’s always the case really when you stop playing football for a little bit; you lose that rhythm in your game, you lose a little bit of your touch and you just need to sharpen up,” he said.
“But it comes with games and playing time – being involved in training and games.
“I’m sure the lads will all be ready and we will get it back to 100 per cent as soon as possible