Local media report that 57-year-old Jose Agostinho Becker had drowned after going for a swim on his property in the city of Lavras do Sul, in the south of the country.
Police confirmed the body of man was found on Wednesday night. No foul play is suspected.
Brazilian club Fluminense said on social media that they were deeply sorry for Jose’s death. Alisson’s brother, Muriel, is a goalkeeper at Fluminense.
Internacional, where both Alisson and Muriel played, also offered condolences.
Liverpool later added: “Liverpool FC is deeply saddened by the tragic death of Alisson Becker’s father, Jose, in Brazil on Wednesday,” said a statement.
“The thoughts of everybody at the club are with Alisson and the Becker family at this incredibly sad and difficult time.
“The club requests that the media respects the privacy of Alisson and his family during this time.”
Alisson’s team-mates Adrian and Virgil Van Dijk both took to Instagram to express their support, with the former writing: “We are all with you hermano.”
The 28-year-old Alisson played at Internacional between 2013 and 2016 before he joined Roma. He left Roma after two seasons to join Liverpool.
Alisson, who was a started for his national team at the 2018 World Cup, won the Champions League and the Premier League with Liverpool.
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