The Premier League champions now sit 12th in the table on 18 points after 12 matches, sitting below great rivals Everton and Manchester United.
Fans called for Slot to be let go after the loss to PSV Eindhoven on Wednesday night, which many believe was utterly embarrassing for a side for spent over £400M in the summer transfer window.
Now, reports suggest that Klopp, who left after nine years at the end of the 2023/24 season, could be set to return to Merseyside to once again take over the side.
Slot guided Liverpool to the title in his first season in charge on Merseyside but last season is irrelevant to the current campaign which sees the Reds on a run of nine defeats in 12 games.
Klopp said in an appearance on the Diary of a CEO podcast last month that it was "theoretically possible" and that the only English team he would ever manage again would be Liverpool.
Slot, meanwhile, revealed this week that he is not worried about the possibility of being fired even if many fans have turned against him which only negates the chances of Klopp returning.
"I am feeling safe, I am OK. I have got a lot of support from above," said Slot. "It would be nice to turn it around and get a victory, of course, but if you are not doing well, then it is normal that questions are asked.
"I am OK with my position. It is not the first time I've been in a difficult position, but it is about time that we turned it around.
"I'm not worried. What I mean by that is my focus is on other things than on my own position. I need to do better, and that's what I'm trying to do every single day."
Liverpool face West Ham United at the London Stadium this Sunday in what is a must win game for Slot whose job is hanging by a string at the moment.