Carragher back for Liverpool this week
Reds boss Rafa Benitez is remaining cautious over Carragher's fitness and will wait until the end of the week before deciding if he will feature at Fratton Park.
He told the club's official website: "We must be careful with Carra, and we will wait until the end of the week to see how well he is.
"He is running again and he will do more training and then maybe we can see if he has a chance to play at the weekend. At this moment, it's still too early to say."