Diaz's parents were captured by leftwing guerrillas of the National Liberation Army in their hometown of Barrancas, Colombia on October 28.
Diaz's mother, Cilenis Marulanda, has since been released but his dad, Luis Manuel, remains with his captors.
Diaz made his first appearance for Liverpool since the incident on Sunday against Luton Town and scored a stoppage time equaliser to salvage a point for Jurgen Klopp's side in a 1-1 draw.
The 26-year-old celebrated his goal with a message underneath his jersey which read: "Freedom for Dad".
He then took to Instagram after the game to plead for his father's release with a message reading: “Today the footballer is not speaking to you. Today Lucho Diaz, the son of Luis Manuel Diaz, is speaking to you.
“Mane, my dad, is a tireless worker, a pillar in the family and he has been kidnapped.
“I ask the ELN for the prompt release of my father, and I ask international organisations to work together for his freedom.
“Every second, every minute, our anguish grows. My mother, my brothers and I are desperate, distressed and without words to describe what we are feeling. This suffering will only end when we have him back home.
“I beg you to release him immediately, respecting his integrity and ending this painful wait as soon as possible.
“In the name of love and compassion, we ask that you reconsider your actions and allow us to recover him.
“I thank Colombians and the international community for the support received, thank you for so many demonstrations of affection and solidarity in this difficult time that many families in my country find themselves living.”
