Carragher insists the board, not manager Arne Slot, will have final say on all transfers this summer.
Speaking on the Overlap, Carragher said: "We know a little bit of what’s gone on behind the scenes. They’ve brought all the old transfer people back if you like. They had a falling out with Klopp, but they’re back now running the club.
"The great thing they built with Klopp, this great team and then they moved away as (Jurgen) Klopp got more power. I think players who have been legends for the club and won the biggest trophies, were given contracts and were allowed to stay at Liverpool longer, too long basically.
"That’s why Liverpool fell off for a little bit and then came back. I think the way they want to run Liverpool is that they are not going to sell their absolute best players.
"But a (Luis) Diaz or a (Cody) Gakpo, who are good players, they wouldn’t want to sell them, but if someone made them an offer, that they think 'That’s more than what we think (they are worth)’ I think that’s the way it will be run now, it will be like 'Oh no, he’s gone and we back ourselves to go again’.
"That’s what I mean in terms of those getting linked. I’m like 'No you wouldn’t want to sell those' but they are probably thinking, 'If you offer us enough money we will do it’. I think the club will be like that now."