Striker Iago Aspas has already been signed from Celta Vigo, while Goal reported on Wednesday that Henrikh Mkhitaryan, Simon Mignolet, Christian Atsu and Luis Alberto are all being targeted by Brendan Rodgers in a £42 million summer splurge.
And Carragher has revealed his former club are moving at pace as they look to assemble their squad in time to hit the ground running in the new campaign.
|15/8||Liverpool are 15/8 with BetVictor to finish in the top four next season
"I spoke to him at the end of the season and he wants to get his business done early. At the moment it looks like Liverpool are trying to get players in as quickly as possible so they are ready for the start of the season.
"They'll look at that Stoke game - Mark Hughes' first game as well, so they'll be desperate to get off to a good start - it's a good game for Liverpool. I'm sure they will be looking to get three points and hopefully use that as a platform to push on.
"The first five or six fixtures look a lot easier, on paper, than they were last season. Arsenal and Manchester City were the first two home games last year; obviously there's a big game in there with Manchester United, the third game.
"In the first couple of games, hopefully they can get three, four, maybe six points and get off to a good start.
"That's certainly what they need because Liverpool need to be doing a lot better in terms of challenging for the top four and getting back into the top four. They really need to make a good start."