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, Chelsea and Real Madrid manager is believed to have a break clause in the three-year contract 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,” added Shearer, scorer of 206 goals for Newcastle over 10 seasons.
“I’m sure he’ll have loads and loads of offers, not only from the Premier League but from around the world.”
Last season, Newcastle needed a last-day victory against West Ham United at St James’ Park to avoid relegation.
Shearer, who as a short-term manager could not prevent the club from being relegated seven years ago, said relegation had been “coming for a while”.
“When you’ve been flirting with relegation for so long the inevitable will happen,” added the former England captain.
“When you don’t address problems that have been glaringly obvious for years then, ultimately, you get what you deserve.”