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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.
"Clube do Povo wishes strength to family and friends in this moment of so much pain."
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.
The thoughts and prayers of everyone at Everton are with Alisson Becker and his family following the tragic news of the death of his father, Jose Becker. 💙— Everton (@Everton) February 25, 2021
Everyone at Manchester City sends their thoughts and condolences to Alisson Becker and his family during this difficult time 💙— Manchester City (@ManCity) February 25, 2021