The Reds made a record-breaking move for the Brazil international over the summer after failing to be convinced by the claims of Loris Karius and Simon Mignolet to their No. 1 spot.
A £65 million ($83m) deal briefly made Alisson the world’s most expensive goalkeeper, with that price tag piling added pressure on his shoulders.
The 25-year-old has looked up to the challenge in his appearances to date, keeping back-to-back Premier League clean sheets, and Crouch believes he could be the final piece of the jigsaw – with Jurgen Klopp having already signed and unearthed top-quality centre-half options.
The former Reds striker wrote in a column for the Daily Mail: “Liverpool was only my home for three years but I've never lost my affinity for the club and their start to the season has me excited.
“I’d love to see them win the title one day. It will go through the roof if they make the final step — and they have got a fantastic chance to do that this year.
“Alisson, the new goalkeeper, was so impressive at Selhurst Park [against Crystal Palace]. His range of passing was outstanding and he made some great saves, too.
“Liverpool have got a proper goalkeeper to go with their two proper centre-halves.
“Virgil Van Dijk got a lot of plaudits but I was just as impressed by Joe Gomez, who has so much assurance.
“I always thought he was a full-back but Joe Allen told me that his future was always going to be in the middle.
“He showed that at Crystal Palace on Monday night with a tremendous performance.”