Coutinho has been heavily linked with a move to Barcelona in recent weeks as they try to replace Paris Saint-Germain new boy Neymar.
Barca are said to have already had a £90million bid turned down by Liverpool, who are desperate to keep hold of their star man.
The Brazil international has not handed in a transfer request at Anfield but is said to be keen on joining the Catalan giants.
And Carragher reckons Coutinho will remain at Liverpool for at least another season before moving to the Nou Camp next summer – like Cristiano Ronaldo when he joined Real Madrid.
Ronaldo promised Manchester United another 12 months at Old Trafford before completing a then-world record £80m move to the Bernabeu in 2009.
Carragher told talkSPORT: “He [Coutinho] hasn’t come out with anything publicly.
“Some players like [Southampton defender Virgil] van Dijk have put in transfer requests and Riyad Mahrez has been vocal at Leicester.
“Philippe Coutinho is not that type of lad. He’s a very quiet lad and I wouldn’t expect a transfer request to come in from him anytime soon.
“I see Coutinho at Liverpool for another 12 months – even if he stays – I don’t think Barcelona will be going away.
“[Cristiano] Ronaldo did the same thing at Real Madrid. Manchester United got another 12 months out of him when they felt he was going to move on.
“I don’t see Barcelona going away. And obviously, Philippe Coutinho is hopefully thinking they won’t go away.”