He had been out since April with a hip issue, and only came on as a late substitute in their 3-1 defeat to Arsenal on Sunday after he had "looked fantastic in training".
He is sidelined again, however, after suffering what Klopp called a muscle injury and will be absent for their Premier League game against relegation-threatened Burnley on Saturday along with the injured Mohamed Salah (31) and Dominik Szoboszlai (23).
Conor Bradley (20) is still with his family following the death of his father.
"The situation with Thiago is obviously not cool," Klopp told reporters. "We don't know the extent yet. It's not good news for him or the club, on top of losing the game.
"It's not a big, big injury, definitely not, but it's something nobody needed."
Bradley's father Joe died three days after he scored his first Premier League goal and had two assists in an electric performance in Liverpool's 4-1 thrashing of Chelsea on January 31st.
"The boy gets as long as he needs with his family," Klopp said. "I think from next week on he will be back in training, but we have to see, if he doesn't feel ready for that, then that's fine as well.
"There's absolutely no rush from us. The only thing we want to do is to support him as much as we can."
Bradley had been brilliant after replacing injured Trent Alexander-Arnold (25) in Liverpool's back line, helping them stay top of the table despite injuries to several key players.
Klopp's team remain top on 51 points after 23 games despite their loss to Arsenal. Manchester City, who have 49 points and a game in hand, can go above Liverpool in Saturday's early game against Everton.
Salah, the league's joint top scorer with City's Erling Haaland (23), is recovering from a hamstring injury sustained while playing for Egypt in the Africa Cup of Nations.
"He's going in the right direction and we hope that he will be part of training next week but we will see," Klopp said. "He's going through his paces now but it's positive. It will be next week or the week after."
Szoboszlai remains out after aggravating a hamstring injury.
"He is running outside in the winter rain but he's not ready for tomorrow," Klopp said. "We have to see with tendons, the players are pain-free pretty quickly, but it's not good he's got it again."
The Arsenal loss was Liverpool's first in 16 league games. Asked if it felt like a setback, Klopp said: "We lost a game and it felt like that, definitely ... but not because the situation with the table, just because we lost the game and we didn't play a particularly good game."
"A few days before, we played in parts our best game of the season, a complete performance against Chelsea. Top class.
"It's always a challenge, we don't take these things lightly and we have to show a reaction."
