The Reds welcome the struggling Clarets to Anfield this weekend as they look to bounce back from a disheartening defeat to Arsenal last time out, but they will be without a number of key players for the visit of Vincent Kompany's side.
Salah has been missing for Liverpool since victory over Newcastle United on New Year's Day after injuring himself at the 2023 Africa Cup of Nations and will not be available for Saturday's encounter.
Speaking in his pre-match press conference about Salah's recovery, Klopp stated: "Right direction. We hope, but we don't know, we hope he will be part or parts of training next week.
"But we have to see. He's going through all the paces now. But look, it's positive. It's either next week or the week after. If you ask him it's next week."
The midfield duo of Szoboszlai and Thiago are also unavailable for Burnley's visit, the latter picking up yet another injury after playing his first minutes in ten months off the bench against Arsenal.
There were rumours suggesting that the Spaniard may not feature again for the Reds this season after sustaining a muscle injury, but Klopp has said that there is no current timeframe on his return.
"Thiago is not cool. He showed a lot of things on LFCTV and looked outstanding, so we took him, let him play for a few minutes," said the Liverpool boss. "It's a muscle issue, we don't know the extent yet but it's not cool. Not good news for him or us."
When asked whether he expected Thiago to play again this season, Klopp responded: "Yes. But we didn't really think about this in the moment, we just read the injury and get the full assessment.
"It's not a big, big injury. Definitely not. But it's something that nobody needed."
On Szoboszlai's fitness, Klopp added: "Dom is running outside in the moment in the winter rain. He's not ready for tomorrow, of course.
"Then we have to see. It's like it always is with these things, pretty quickly the player is pain-free. It's pretty much the same as what he had before. That's obviously really not good that he got it again.
"Is it Brighton [when he returns]? Is it the [Carabao Cup] final? Is it after the final? I don't know in the moment."
The aforementioned three will be huge misses for Liverpool as they look to bounce back from last weekend's disappointment, with Ibrahima Konate suspended and Conor Bradley still absent after the death of his father.
There are also injuries to Joel Matip, Kostas Tsimikas, Stefan Bajcetic and Ben Doak, while Klopp suggested that there was a 'flu' going around the Liverpool training ground that may impact the availability of players.
In slightly more positive news, Wataru Endo is fit and ready to return this weekend after travelling to the Asian Cup with Japan.