The former Manchester United captain does not believe his former club are on course to win the title, even though Ole Gunnar Solskjaer's side are currently sitting top of the table after a 0-0 draw against Liverpool on Sunday.
Instead, Keane is backing Klopp's side to bounce back from their mid-season slump to storm back to the top of the table.
"I'm still sticking with Liverpool," Keane told Sky Sports. "Obviously they've had a difficult spell for them because of the standards they've set in the last few years.
"Their attacking players are brilliant, I've said they've lost their spark but I think they'll get that back. We've seen every team have their ups and downs this season. I think they have enough quality, enough energy, I look at Klopp, I'm sticking with them."
Meanwhile, Liverpool great Jamie Carragher believes a lack of pace is an issue for Liverpool's misfiring front three of Mo Salah, Sadio Mane and Roberto Firmino.
Liverpool have now gone three Premier League games without at goal and Carragher told believes that there are a variety of reasons for a slump in form for Klopp's side.
"When Jurgen Klopp initially came in there was a problem against teams who defended deep against them, certainly at Anfield. And that was the days when they had Philippe Coutinho as well," he stated.
"They would drop points in those games and that seemed to have gone away in the last couple of years. And at this moment it looks like they are having problems breaking teams down. They have played their last three fixtures against teams where you would expect them to have maybe seven points out of nine in those games.
"People talk about missing Van Dijk defensively. They haven't missed him defensively really, when you look at the record. But of course you miss him, for lots of different reasons, and actually on the ball…in terms of building from the back and starting the attack,
"Liverpool mixed it up really well, playing different balls last season. Playing good football, but mixing it up well. They would be direct at times in a football sense, where you'd see Van Dijk play that ball over the top or switch the play and it would be really quick.
"The football at the moment just feels a bit slower I would say and I think a lot of that is the build up from the back. Van Dijk is unique in being a great defender and (having) his ability on the ball.
"I think teams that want to stop Liverpool and are maybe coming for a draw are finding it easier – to regroup and be compact and not be moved about as much and as quickly, certainly because of VD being out."
Liverpool v Burnley is live on Sky Sports this Thursday at 8pm.