Salah was ruled out of Sunday’s 3-0 win over Leicester after testing positive for the virus while away on international duty with Egypt earlier this month.
The Liverpool manager confirmed Salah produced a negative test on Sunday prior to the Leicester match and could rejoin the group on Monday after a period in self-isolation, having initially tested positive on November 13.
Salah will undergo further testing in the coming days, with Liverpool’s next match at home to Atalanta in the Champions League on Wednesday.
Speaking after the win over Leicester, Klopp said: “That’s what I’ve heard, a negative today.
“I think from now he is pretty normal in all the testing. Tomorrow we have UEFA testing and I am pretty sure he will be in that.
“He can train with us tomorrow. There are two tests in the next two days so he will be tested.”
Salah’s availability will come as a welcome boost for Klopp, who is already without a number of senior players through injury – including defenders Virgil van Dijk, Joe Gomez and Trent Alexander-Arnold.
There are also concerns over midfielder Naby Keita, who was forced off against Leicester with a hamstring problem.
However, Klopp says it is too soon to know the severity of the injury.
“He felt his hamstring and was not able to play on, otherwise he would have stayed on the pitch,” he said.
Klopp also confirmed Xherdan Shaqiri missed the match after a scan revealed he had a slight muscle injury after returning from international duty with Switzerland.
“How I know it, Shaqiri had a little muscle injury at the national team which he didn’t really realise,” said Klopp.
“So now he trained with us, we gave him a day off and then he came back. He was involved in a session but not fully involved.
“After that he felt it a little bit. He had a scan and it found that he has an injury from five or six days ago. Nobody knew about that, not even Shaq, but that’s how things are sometimes, so he was not able to be involved.”
