The Anfield club has won just four of their last 14 games, leading to widespread speculation about the future of current boss Slot.
Carragher, when asked on The Overlap Fan Debate about rumours of Gerrard potentially replacing the Dutch manager, dismissed the idea with a simple response.
"No, I wouldn't imagine," he said.
He recognised Gerrard's managerial experience at Villa and his successful stint at Rangers, but expressed doubt about the legend returning to Liverpool as manager.
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He said: "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."
According to Carragher, the fanbase's frustration with the club's form this season means they want Slot to succeed.
However, this raises the concern of how long poor form and support for Slot can coexist.
"They're on such a bad run, the flipside of that is then how long does it carry on?" Carragher added.
Steven Gerrard pulled out of the running for a return to the managerial hot-seat at Rangers at the end of October.
The position was later filled by Danny Rohl, who took over from Russell Martin.
Rohl started off strong, winning his first four league games.
However, Rangers' form has faltered with recent draws against Falkirk and Dundee United, with the latter game ending 2-2 at Tannadice on Wednesday evening.
This Saturday sees Rangers face Kilmarnock, as they look to improve on recent results.