German midfielder Can blasted in his his fourth goal of the season to edge the Reds past Burnley on Sunday.
But the former Bayer Leverkusen man is out of contract at the end of next season and is stalling on a new deal.
Kop legend Carragher thinks he could be sold in the summer if he fails to come to an agreement.
He said: “Can’s big problem is that I don’t think he’s a versatile player but he’s played in four or five positions for Liverpool.
See Klopp’s full press conference after Liverpool’s 2-1 win
“The only position I think he can play is the one he played [against Burnley], the sitting midfielder, because he needs legs around him. [Klopp] is playing Jordan Henderson ahead of him.
“Now, he’s got a contract situation at the moment, Emre Can. Is he going to sign it? Is he not? I think he may have 12 months at the end of the season.
“So there is a good chance he may not be here next season. I don’t see, when the first XI is picked, where else he can play except that role.
“That role is for the captain Jordan Henderson, who I can see how much he is missed in the last three or four games he’s been out.”