At least two of the 10 assailants who broke into the embassy and interrogated diplomatic staff have been identified and have connections to the USA intelligence agency.
Spanish investigators ruled out the possibility that the attack was by common criminals as the attackers knew what they were looking for, taking only computers and cellphones.
The CIA has denied involvement in the attack.
Sources close to the investigation reportedly told El País that the operation was planned perfectly, as if by a "military cell".
The attack on February 22 was initially reported by Spanish online newspaper El Confidencial on February 27, prompting Spain's National Intelligence Center and police intelligence division to investigate the case.
The freakish - and movie-like - incident occurred on February 22, when a group of men attacked the North Korea's mission to Spain, located in Madrid. A woman managed to escape from a window on the second floor and her screams for help were heard by a neighbor, who contacted the police. Soon after officers arrived, the 10 assailants sped away. Sources in the Spanish government believe that if the CIA's involvement in the attack is confirmed, it will be regarded as "unacceptable" actions by the ally. They were later found abandoned on a nearby street.
El Pais said that sources believe the attack was meant to get information on former North Korean Ambassador to Spain Kim Hyok-chol, who negotiated nuclear disarmament plans with US special envoy Stephen Biegun ahead of the US-North Korea summit in Hanoi on February 27-28.
Former North Korean ambassador to Spain, Kim Hyok Chol, in a file photo from 2015.
El País pointed out that the robbery took place five days before Donald Trump's second summit with the North Korean leader, Kim Jong-un.
He was expelled by Spain in September 2017 in protest at North Korean nuclear tests and has not been replaced.
But Mr Kim is now serving as a key envoy in North Korean talks with the United States, and helped organise the recent summit in Vietnam. The meeting, aimed at securing North Korea's nuclear disarmament, ended in failure without any agreement on a timetable for disarmament or on future negotiations.