The Reds have already rejected two Barcelona bids for the Brazilian and Carragher believes he will stay.
“I still think he will be at the club and I would keep him," he said on Sky Sports.
“Luis Suarez put in a transfer request, stayed 12 months and played the best football of his life."
Carragher is not pleased with reports surfacing that Coutinho, who is currently absent with a back injury, is not getting on with manager Jurgen Klopp, believing they cross a line.
“I've said before there is not a problem with him wanting to go to Barcelona, 99 per cent of footballers all round the world will want to do that," the former defender added.
“When a transfer request goes in, the supporters of that club feel it a little bit more, but again, it's part of the game.
“But the stuff about not getting on with Klopp, these stories getting fed out, that's where I think that crosses the line.
“I spoke about (Virgil) Van Dijk (of Southampton) where he's not playing or not training, there's no problem wanting to move, it's part of the game but there is a line you don't cross where you ruin your own reputation and that needs to stop.
“Talking about Klopp and not getting on and someone feeding the story.
“Stop that, you've put your transfer request in, now it's up to the club. You've signed a five-year deal, they will make the decision.
“The decision from the owners that they've stated is that he's going to stay."