The Egyptian is enjoying one of the finest debut seasons in history following his move from Roma in the summer. He sits second on the Premier League goal-scorers list with 21 goals, one behind Harry Kane, and has scored 28 across all competitions.
His performances have piqued the interest of Real Madrid, but Carragher believes Salah will remain at Anfield for the next few years at least.
The Liverpool legend told talkSPORT: "Well, fingers crossed. He's only just arrived so we want to enjoy him for as long as we can.
"It's very difficult, and in some ways you have to sort of just accept it and try and get the biggest fee you can possibly get - as Liverpool did with Coutinho.
"I'd expect Salah to be at the club for the next few years. The contract that he signed and the position Liverpool are in with Coutinho just going, they can't afford to let another big name player go."