Benitez has been appointed as the new Newcastle manager following the dismissal of Steve McClaren on Friday.
There is a distinct possibility that Newcastle could get relegated to the Championship at the end of the season.
Former England international defender Carragher, who worked with Benitez at Liverpool, believes that the Spaniard would not be the manager to guide the Magpies back to the Premier League if they get relegated.
“If you're a fan and Newcastle went down, you wouldn't want Rafa, you'd want someone that has experience in that league and has success in that league,” Carragher told Sky Sports. “Rafa won't want to be there.”
Benitez is one of the most decorated football managers in the world and knows the Premier League inside out.
The Spaniard achieved quite a bit of success at Liverpool, guiding the Merseyside outfit to FA Cup, Champions League and UEFA Super Cup glory.
The former Chelsea boss does not know the Championship, and it would not make any sense for him to manage a team in the second tier of English football given his pedigree.