Jurgen Klopp has spent big this summer in an effort to push his side closer to the top-flight crown, with those at Anfield having finished 25 points off record-breaking pace last season.
Brazil international Alisson is among those to have been drafted in, with a £67 million ($87m) deal making him the most expensive goalkeeper in history.
The former Reds captain wrote in a column for the Sunday Times: “A goalkeeper was clearly a priority and Liverpool have broken the world record for that position by signing Alisson from Roma for £67m.
“So he’s not coming with 300-400 games at the highest level under his belt and, despite the fee, there has to be a question mark against him.”
While Souness is yet to be convinced by Alisson, he has been impressed by the work overseen by Klopp.
“If their signings work out, if the goalkeeper is a proper one and the new midfielders are workaholics who can handle our football, Liverpool will push City all the way in the two big competitions this season - the Premier League and the Champions League,” added Souness.
“They are the team that City will fear most, unless somebody goes on a late summer spending spree. They must put Pep Guardiola's side under pressure and see if they crack.”
Liverpool have one more friendly fixture to take in before competitive action resumes, against Torino on Tuesday.
They will open their Premier League campaign at home to West Ham on August 12, before going on to face Crystal Palace and Brighton in the first month of the season.