Manager Rafael Benitez told the club's website: "We thought it would be two or three weeks and he's only 12 or 13 days into that so there's no point in him going.
Related ArticlesFernando Torres exclusiveLiverpool will pip City in race for fourth placeLiverpool 2 Manchester City 2Liverpool face winter of woeLiverpool to make top four, says Rafael Benítez"The next few days will decide if he is fit for Everton (on Sunday), but at this moment there are no guarantees."
Liverpool need to beat Debrecen to keep their hopes of reaching the knockout stages alive, although a victory would be rendered meaningless if Fiorentina beat Lyon.
Captain Steven Gerrard has insisted that he and his squad can still salvage something from a season that started with high hopes of a sustained challenge for Liverpool's first league title since 1990.
"The mood in the camp is really good, although we know our position in the table isn't good enough," Gerrard said. "But we have faith in our ability. We know we can put things right."
He added: "It's been a frustrating few weeks because as soon as I was fit we had the international break. I've been desperate to play and can't wait to really get going properly again."
Gerrard started his first game in a month on Saturday when Liverpool drew 2-2 at home to City and he is expected to start again in the Hungarian capital, possibly with the help of a pain-killing injection.
Benitez admitted it was frustrating for Liverpool to have lost control of their own destiny. "A lot depends on Fiorentina and Lyon, but the main thing for us is to concentrate on our game and see what happens," he said.
"We have to prepare our game because we don't have any influence over the other one. If we can do our job and win, we'll see.
"I think we can do it. We have some players coming back from injury, so hopefully with a bit of luck we can progress.
"It's football, so you never know. We'll see if we can keep going in the Champions League."
Jamie Carragher, who was also struggling with injury at the weekend, was in Liverpool's 18-man squad that travelled to Budapest.
Glen Johnson, who missed the City game with a calf problem, was also in the party, while Albert Riera's hamstring injury meant he was left behind for further treatment. Daniel Agger has recovered from a head injury sustained at the weekend.