The Reds have been linked with signing the Bayern Munich midfielder for a deal rumoured to be in the region of £35 million.
Reports from reliable publications in Germany and elsewhere have even gone as far as to suggest Thiago has agreed personal terms with the Premier League champions.
Local journalists have admitted Liverpool are interested in the 29-year-old, but have maintained there has been no contact between the two clubs.
Speaking after Liverpool’s 2-0 win over Aston Villa on Sunday, Klopp was asked about his thoughts on the Spanish international.
“Would you be surprised if I don’t give an answer on that, just because I never answer these kinds of questions,” Klopp said.
“Thiago Alcantara is a really good player. Like a lot of other players out there, I like (him) a lot.
“But that’s all I have to say about that.”
Meanwhile, Athletic journalist James Pearce says he has been told the deal is “unlikely but not impossible,” although no contact has been made with Bayern yet.
“I’ve been told ‘unlikely but not impossible.’ Klopp rates him highly,” Pearce wrote in a Q&A.
“He’s available and keen on moving to the Premier League. However, his age, injury record & current options in midfield count against it happening.
“[There has been] no contact with Bayern yet.”
It remains to be seen what happens in the coming weeks and months. Thiago’s quality is undeniable, but his signing would break the mould in many ways with Klopp’s usual policy of bringing in younger and more athletic players.