News emerged on Saturday that Diaz's parents had been captured in Colombia after a vehicle they were travelling in was intercepted by two armed men.
Diaz's mother, Cilenis Marulanda, has been released but his dad, Luis Manuel, remains with his captors.
"On the instructions of the Minister of Defense, a reward of up to 200 million pesos will be given to anyone who gives us information that allows us to find the whereabouts of Mr. Luis Díaz," police general William Rene Salamanca said.
Diaz was left out of the Liverpool squad for Sunday's 3-0 win over Nottingham Forest following the breaking news, with manager Jurgen Klopp admitting afterwards that his squad had been unsettled.
"We had to obviously make a late change because of the private situation involving Luis Diaz," Klopp explained.
"It's a worrying situation for all of us and it was a pretty tough night. I have never had that before. It's a new experience I never needed."
"Liverpool Football Club can confirm it is aware of an ongoing situation involving the family of Luis Diaz in Colombia," a statement from the club read on Sunday.
"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."
