Liverpool had been hoping that they could swoop in before the start of the tournament in Russian Federation and confirm the arrival of a new goalkeeper, a position which is in dire need of improvement after Loris Karius' performance in the Champions League final.
Speaking to Italian radio station Tele Radio Stereo, Tafferel said: "Alisson is very happy at Roma and the rumours of a transfer are just rumours".
'There are many possibilities on which we are working, but always together with Roma and with respect to my club.More news: Spain offers to take migrants stranded in Mediterranean Sea
All Alisson did confirm was that his agent was in talks with a few clubs, but he said that if nothing is confirmed before the World Cup, he will wait until after the tournament to decide his future as he wants to focus on helping his country with the famous competition yet again. "We'll see if anything happens this week".
Liverpool are reportedly keen on signing the Roma goalkeeper.
He is likely to be Brazil's No 1 when they begin their World Cup campaign against Switzerland on Sunday.
Former Brazil goalkeeper Claudio Taffarel believes that Liverpool target Alisson can become as good as Thibaut Courtois and David de Gea.
"If it's not before the first game, it will be after the World Cup, that's my thinking 100 percent", Alisson continued.