The Anfield club have won just four games out of their last 14.
Such form has led to widespread speculation over the future of boss Slot.
When recently appearing on The Overlap Fan Debate, Carragher was asked if rumours of Gerrard potentially coming in to take over from the Dutchman were true.
"No, I wouldn't imagine," he replied. "He's been a manager at Villa and had great success at Rangers as well.
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"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 flipside of that is then how long does it carry on?"
Gerrard pulled out of the running to become the new Rangers head coach at the end of October. Danny Rohl eventually took over from Russell Martin.
The German won his first four league games in charge, although his side drew 0-0 with Falkirk at the weekend before following that up with a 2-2 stalemate against Dundee United at Tannadice on Wednesday evening.
Rangers are back in action this Saturday as they travel to face Kilmarnock.