According to widespread reports, the 57-year-old was swimming close to his holiday home in Brazil on Wednesday when he was reported missing.
A search was launched and his body was found.
Internacional, for whom Alisson's brother Muriel also used to play, tweeted: "It is with great sadness that we received the news of the death of Jose Agostinho Becker, father of our former goalkeepers Alisson and Muriel.
É com muita tristeza que recebemos a notícia da morte de José Agostinho Becker, pai dos nossos ex-goleiros Alisson e Muriel. O Clube do Povo deseja força aos familiares e amigos neste momento de tanta dor.— Sport Club Internacional (@SCInternacional) February 25, 2021
"Clube do Povo wishes strength to family and friends in this moment of so much pain."
Liverpool tweeted an image of the Alisson accompanied by the club's motto, "You'll never walk alone," and a heart emoji.
Brazil international Becker moved to Anfield from Roma in 2018, after appearing for his country at the World Cup in Russia.
The 28-year-old won the Champions League in his debut season and helped Jurgen Klopp's side to the Premier League title last term.