The pair did not figure in Liverpool’s victory at Norwich City last weekend having returned to pre-season training later than many of their teammates due to their involvement at Euro 2020.
However, Klopp confirmed during his pre-match press conference that Henderson and Thiago could come into contention for Saturday’s meeting with Burnley having participated in a behind-closed-doors friendly match last Sunday at Anfield.
The manager said: “They are much closer, yes. They look fine, now we have to make the decision.
“They looked really good in the game and looked good in the training week, so it’s up to me to make some decisions.”
Meanwhile, Klopp was asked about Fabinho after the passing of his father earlier this week.
“I would like to say it’s a private situation,” he said. “Fab is here and is doing what he is able to do and that’s it pretty much.
“We all feel for him, we all feel with him and we give him and his family our condolences. We try to give him all the warmth, all the love we have in this moment and that’s it, the rest is private.”