Jose Becker, died after drowning in a lake near his holiday home in Brazil, local police said.
The 57-year-old is said to have been swimming at a dam near his property in the afternoon on Wednesday.
The club led tributes to the former goalkeeper, with a statement which read: “ Liverpool FC is deeply saddened by the tragic death of Alisson Becker’s father, Jose, in Brazil on Wednesday.
“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 privacy of Alisson and his family is respected during this time.”
It is understood Klopp, who lost his mother recently and was unable to travel to the funeral in Germany, has spoken at length with Alisson, and will offer support in the coming days.