The 25-year-old, who was the Selecao's first-choice stopper at this summer's World Cup finals, arrived at Anfield from Roma on Thursday evening in a record deal for a goalkeeper.
Alisson has already talked about the part former Roma teammate Mohamed Salah played in persuading him to join the Reds, and fellow Brazilian Firmino was also keen to see a move go through.
"I spoke to him before things really started to happen," he told the club's official website. "When the negotiations became official I spoke to him and only heard good things about the club and the city.
"He feels really at home here. He's loved by the fans and popular with his teammates. He said if I were to come, I'd be really happy as well."
Alisson's arrival on Merseyside could lead to Simon Mignolet being sold, while Danny Ward has already been offloaded to Leicester City.