Colombian police are offering a cash reward to anyone who can help locate Luis Diaz's father.
Media in the South American country reported the Liverpool forward's father had been kidnapped in Colombia on Saturday.
The authorities have offered a £40,000 reward for information leading to his rescue.
More than 120 soldiers, plus police, searched northern Colombia for him on Sunday, with reports suggesting armed men had taken the football player’s dad - also called Luis Diaz - and the player’s mother, Cilenis Marulanda.
According to Colombia's president, Gustavo Petro, she has been rescued and returned to safety.
In a statement, the Colombian army said it had set up roadblocks, used drones, helicopters and a plane with radar in the search for Mr Diaz.
In a social media post on Sunday offering a reward for information about Mr Diaz’s whereabouts, Colombian national police said: “By decision of the Ministry of National Defence and the Minister of National Defence of Colombia a reward of up to $200 million pesos is offered for information that allows the rescue of Mr. Luis Manuel Diaz and the capture of those responsible for this criminal action."
A photo of Diaz Sr's was also posted alongside details of the reward.
Officials have not confirmed reports of kidnapping, but local media have reported the couple were taken by armed men on motorcycles at a gas station in their home town of Barrancas, in the north of the country.
The possibility that Mr Diaz could have been taken to Venezuela is also being explored, according to reports.
Diaz did not play in Sunday’s Liverpool match against Nottingham Forest as the search for his father continues.
Liverpool manager Jurgen Klopp dedicated Sunday's 3-0 Premier League victory over Nottingham Forest to Diaz, saying they had won “for our brother".
Player Diogo Jota held up the Colombia player's number seven shirt after Liverpool scored its first goal in a gesture of solidarity.
The club said in a statement that it was “aware of an ongoing situation" involving Diaz's family, adding his welfare “will continue to be our immediate priority".
