The 27-year-old Brazil midfielder's wife, Rebeca Tavares, confirmed on social media that his father has died.
Klopp said: "I would like to say it's a private situation. Fab is here and is doing what he's able to do and that's it pretty much.
"We all feel for him, we all feel with him. We all gave him and his family our condolences and tried to give him all the warmth, all the love, we have at this moment and that's it. The rest is private."
Klopp revealed Jordan Henderson and Thiago Alcantara could return to action after playing in a behind-closed-doors game against Aston Villa this week.
Both midfielders missed out at Carrow Road last week having returned late to pre-season after their involvement at Euro 2020.
"They're much closer. They look fine. Now we have to make a decision," Klopp said. "They looked really good in the game and this week in training. It's now up to me to make some decisions."
Liverpool' s 68-game unbeaten home run in the Premier League was ended in a 1-0 defeat to Burnley in January last season, but Klopp insisted it would have no bearing on Saturday's match.
"Not in a moment, sitting here to be honest," he said. "I didn't even think about it. Now you have told me, that's something I didn't like.
"It was a strange one. Yes we lost it, Burnley won it, that's how football is, so well deserved. But it obviously has nothing to do with the game now."
Klopp said he was excited by the return of fans to Anfield and was not looking for "revenge" against Sean Dyche's side.
"We will try everything to have our first home game in front of our crowd for the first time in 520-something days I think and we want to enjoy that," Klopp said.
"Football is only possible to enjoy when you play in a positive way, when you just go for it. There are no guarantees out there, not at all, especially not against Burnley because they can make your life really uncomfortable."