Liverpool’s win over West Ham United leaves them 8th in the table, three fewer than third-placed Chelsea and four below second-placed Manchester City who trail leaders Arsenal who are five points clear.
The Reds have had a mixed start to the season, with many fans calling for Slot to be sacked after the Dutchman led the club to nine defeats in 12 matches before they faced the Hammers.
One candidate touted to replace Slot was former captain Gerrard, who Carragher says would not be the fans’ first pick considering his lack of experience in the top flight.
“No, I wouldn’t imagine. He’s been a manager at Villa and had great success at Rangers as well.
“He’s a legendary figure, and he’s back, floating down Liverpool. I don’t think most Liverpool fans will be screaming for Steven Gerrard – everyone is desperate for it to work for Arne Slot.
“They’re on such a bad run, the flip side of that is then how long does it carry on?”
Slot’s side host Sunderland on Wednesday before Saturday's trip to Leeds, who are in the relegation zone. Both are must win games if Slot is to keep not only his title dreams alive but also his job intact as fans keep a close eye on results in what could have been a year spent defending their Premier League title.