The striker returned to full training at Melwood in the week after a pre-season injury and is likely to be available for selection against a Palace side seeking their fourth straight Premier League victory at Anfield.
“Yesterday Daniel was part of the complete session and looked really good, but always after injuries you have to wait to see how the player reacts to this intensity,” Klopp told Liverpoolfc.com.
Meanwhile, Klopp revealed there has been “no change” in Nathaniel Clyne’s condition as he continues his rehabilitation programme from a back issue.
The elephant in the room with Liverpool at the moment is Philippe Coutinho, who is set to miss his third game of the season with a back injury.
After Wednesday night’s Spanish Super Cup defeat to Real Madrid, Pep Segura, Liverpool’s former academy technical manager and now Barcelona’s general manager, said on Spanish television:
“We are close to Coutinho and (Ousmane) Dembele.
“We are discussing their deals but do not know when it will be done.” Asked if he expected them to sign, he added: “Yes, we expect it.”
However, Klopp is adamant there have been no more developments and the two clubs are not even in discussions.
“I saw the game (Real-Barcelona) but I forgot to watch the interviews afterwards. Nothing to say from our side,” said the Reds boss.
“I don’t know why other people are saying what they are saying. I don’t even know them – especially this guy, I’ve never even met him.”
Asked whether there had been any subsequent talks, Klopp added:
“I am not sure I have to answer this because we have said what we have to say, or the club said what we have to say.
“No news from me because no one told me anything different since we spoke last time about this.”
There have been suggestions Coutinho could agitate for a move by effectively going on strike but while he is still injured that is impossible.
Klopp was asked about the prospect of this and the Brazil international’s general attitude.
“I have nothing to say about his attitude because since he has had a back problem he has not been in training,” he said.
“I asked the medical department how he is doing and there are no complaints so that is how it is. There is nothing bad to say.
“We are all not silly. We know it is a very difficult situation but there is nothing new to say.
“It is not always easy for me to say the 100 per cent truth – even though I don’t like to – but it is exactly how I say it because that is how it is in the moment, nothing else.”