Firmino was signed for an initial £21million from Bundesliga club Hoffenheim this summer, with the fee potentially rising to £29million through clauses.
The Brazilian could become the third most expensive Liverpool signing ever as a result, behind just Andy Carroll (£35m) and new team-mate Christian Benteke (£32.5m).
The 23-year-old was officially unveiled by the Reds on Wednesday after taking an extended leave following the Copa America, and is expected to share the goal burden this season after scoring 49 in 153 appearances from attacking midfield for Hoffenheim.
But club legend Carragher has fired a warning to Liverpool fans expecting him to be an instant success, saying he is just as likely to “be another Alberto Aquilani” as he is to emulate Suarez.
Italian midfielder Aquilani was signed for around £17million from Roma to replace Xabi Alonso in 2009 but, despite the fanfare, struggled during his Merseyside spell and managed just one disappointing season.
Writing in his Daily Mail column, Carragher has warned that the same fate could befall Firmino: “Though 95 per cent of Liverpool supporters have never seen Firmino in action – YouTube doesn’t count – they believe he is already on his way to becoming an icon.
“He comes from Brazil, his style is similar to Luis Suarez’s and his form for Hoffenheim was brilliant, leaving fans saying: ‘Imagine what he’ll be like for us!’
“That is the mystique of buying players from abroad. Firmino could well be another Suarez; he could also be another Alberto Aquilani.”