Newcastle's second relegation from the Premier League in eight years was confirmed on Wednesday.
Shearer told BBC Radio 5 live: "A guy of great stature, a world-renowned coach with his CV managing in the Championship? I can't see it happening.
"I'd love to be wrong. It would be brilliant if he was to stay."
Benitez succeeded the sacked Steve McClaren with Newcastle 19th in the table but could not save the club, winning two of nine league games.
The former Liverpool and Real Madrid manager has a break clause in the three-year deal he signed in early March, which means the 55-year-old's future with the club is uncertain.
"I know it's a huge football club and I know he's been very impressed with how the fans have taken to him but I'd be amazed if he stayed as I'm sure he'll have loads and loads of offers, not only from the Premier League but from around the world," added Shearer, scorer of 206 goals for Newcastle over 10 seasons.