Diaz’s mother was rescued but his father remains missing, Colombia’s president Gustavo Petro said.
Liverpool have confirmed they are aware of an “ongoing situation involving the family of Luis Diaz” and said the 26-year-old’s “welfare will continue to be our immediate priority”.
Colombian authorities have said Diaz’s mother, Cilenis Marulanda, was rescued by police in the city of Barrancas.
The country’s police director said Diaz’s father remains missing but used a video address to say he is using every agent to find him.
Diaz’s parents were driving home when they were stopped by the gunmen, the police director said.
Meanwhile, Colombia’s football federation released a statement urging authorities to find and rescue Diaz’s father.
Liverpool said in a statement on Sunday morning: “Liverpool Football Club can confirm it is aware of an ongoing situation involving the family of Luis Diaz in Colombia.
“It is our fervent hope that the matter is resolved safely and at the earliest possible opportunity. In the meantime, the player’s welfare will continue to be our immediate priority.”
Liverpool host Nottingham Forest in the Premier League this afternoon.