Luis Manuel DÃ­az was seized at gunpoint along with his wife on Saturday.
The player's mother was left behind in a car by the kidnappers as police closed in, but the gunmen dragged away his father.
Hundreds of police and soldiers have been deployed to free him.
Police had originally said that a criminal gang was most likely to blame.
But on Thursday, a government delegation which is currently engaged in peace talks with the rebel group, said that it had "official knowledge" that the kidnapping had been carried out by "a unit belonging to the ELN".
A representative of the group has reportedly said the group will free DÃ­az's father in the coming days.
The ELN is Colombia's main remaining active guerrilla group. It has been fighting the state since 1964 and has an estimated 2,500 members.
It is most active in the border region with Venezuela where Luis Manuel DÃ­az and his wife Cilenis Marulanda live.
CCTV footage showed their car being followed by men on motorbikes on Saturday afternoon.
The couple was accosted by the gunmen as they had stopped at a petrol station in their hometown of Barrancas, in the northern province of La Guajira.
The kidnappers later abandoned Luis DÃ­az's mother in a car as police closed in, but dragged away his father.
Police have focussed their search on the SerranÃ­a del PerijÃ¡, a mountainous area straddling the Colombia-Venezuela border.
They have found two motorbikes and a car they think were used in the kidnapping but have yet to pinpoint Luis Manuel DÃ­az's whereabouts.
In his statement[in Spanish], the head of the government delegation negotiating with the ELN, Otty PatiÃ±o, demanded the "immediate release of Luis Manuel DÃ­az.
"We remind the ELN that kidnappings are criminal acts which violate international humanitarian law and that it is their [the ELN's] duty as part of the current peace process to not only stop engaging in kidnappings but also to forever stamp them out," the statement reads.
Previous attempts at reaching a peace deal with the ELN have failed but as part of President Gustavo Petro's strategy for "total peace", his government restarted talks with the guerrilla group.
Earlier this year, the two sides agreed on a bilateral six-month ceasefire which came into force on 3 August.
The kidnapping of Luis DÃ­az's father has caused outrage in Colombia, where the player - who is part of Colombia's national team - is immensely popular.
On Tuesday,hundreds accompanied Cilenis Marulanda on a march to demand his release.
His Liverpool team has also shown its unwavering support, with manager JÃ¼rgen Klopp dedicating Sunday's 3-0 Premier League victory over Nottingham Forest to DÃ­az, saying they had won "for our brother".
The Colombian government says that the father of Liverpool footballer Luis DÃ­az was kidnapped by left-wing rebels of the National Liberation Army (ELN).