It was reported that Jose Agostinho Becker drowned on Wednesday while swimming close to his holiday home in Brazil.
The 57-year-old was reported missing and, following a search, his body was found.
Alisson wrote in a message on Twitter on Thursday: "I would like to thank everyone for the messages and tributes to my beloved father!
"Our family feels loved by everyone! May God bless each one's lives!"
The Brazil international has played 27 games in all competitions for Liverpool this season.
The Reds play bottom-of-the-table Sheffield United at Bramall Lane on Sunday.
Jurgen Klopp's side are seeking to halt a four-match losing run in the Premier League that has seen the defending champions slip to sixth place.