The right-back is being linked with a move away as a free agent in the off-season.
Alexander-Arnold is a huge target for Real Madrid, who the Reds beat 2-0 on Wednesday night in the Champions League group stage.
Speaking on CBS Sports, former defender Carragher stated: “ think the reaction to him will be different to Salah when we start talking about his (contract situation).
“I think he will get a lot more criticism because when you're a local player a lot more is thought of you. And I think that the feeling of the Liverpool supporters will worry him a little bit and I think he'll end up signing.”
Carragher added: “I think he will be very worried about the reaction if he didn't sign and he left on a free to go to, say, Real Madrid.
“I think the feeling with Liverpool supporters would be a lot different to what it has been of late, in the last few days, with Mo Salah... because he's a local player.
“I’ve seen it with Steve McManaman when he went to Real Madrid on a free (in 1999). He was a great player for Liverpool. So was Michael Owen.
“Actually, Michael Owen did an interview today when he said that at times when he goes back to Anfield he doesn't feel welcome and secure going back there. Some of that is to do with playing for Manchester United (between 2009 and 2012), I get that. But a lot of it is to do with leaving Liverpool. And he didn't leave on a free, he left for £12M (when he signed for Madrid in 200).
“I think that will be in the back of Trent's mind at the moment. And I think that when you are a local player you don't want to lose the legacy that he's already got.
“He's been there since he was a boy, he's 26 now and he's won everything. You don't want to lose that and I think he'll sign.”
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