Jurgen Klopp’s side host Arsenal (4pm) looking to continue their unbeaten start to the Premier League campaign.
Arsenal come into the match having lost their last Saturday’s game against Stoke 1-0.
Liverpool, however, have won their last three in all competitions and qualified for the Champions League group stage by overcoming Hoffenheim 6-3 on aggregate in the play-off earlier this week.
Games between these two sides often produce goals and Carragher is expecting an open encounter on Merseyside.
The former defender is backing his former team to continue their run and pile more misery on Arsenal.
“I fancy Liverpool at home,” Carragher said on Sky Sports.
“I think under Jurgen Klopp Liverpool’s record against the top sides, especially at Anfield, is fantastic.
“The problem is when you’re coming up against a Crystal Palace that were here last week, it was a difficult game. It was a big win for Liverpool.
“But I think on the back of what happened last week at Stoke and what happened midweek with Liverpool in terms of qualifying for the Champions League, I fancy Liverpool today.
“It will be an open game and that’s maybe a criticism of both sides, that at times they are too open.
“But it makes for a great game, hopefully for ourselves.”