But Taffarel told Tele Radio Stereo: "Alisson is very happy at Roma and the rumours of a transfer are just rumours".
He is likely to be Brazil's No 1 when they begin their World Cup campaign against Switzerland on Sunday.
As many national team coaches forbid transfer activity during their World Cup campaigns, players that will be traveling to Russian Federation this month will either need to have arranged any potential moves before the tournament or wait until they return home to finalise remaining details.
Former Brazil goalkeeper Claudio Taffarel believes that Liverpool target Alisson can become as good as Thibaut Courtois and David de Gea.More news: Kim Kardashian West shares glimpse at Kanye’s birthday bash
He added: "I think everything will be resolved before the start of the World Cup, that's what I want".
The Roma custodian wants his future sorted out before the start of the World Cup, enabling him to give Brazil his fullest commitment and concentration.
'The truth is that I left everything in the hands of my agent.
The Brazilian is on the Reds' radar as Jurgen Klopp seeks a new goalkeeper for the new Premier League season. "We'll see if something happens during this week".More news: Rumor: Celtics 'Scared' Kyrie Irving Might Leave in 2019 To Join Knicks
"If it's not before the first game, it will be after the World Cup, that's my thinking 100 percent", Alisson continued.
'There are many possibilities on which we are working, but always together with Roma and with respect to my club.
I'd love both obviously.More news: Larry Kudlow calls Justin Trudeau's verbal attacks 'amateurish,' a 'betrayal'