The film allegedly shows the military head of the Revolutionary Armed Forces of Colombia (FARC) Jorge Briceno -- code name Mono Jojoy -- talking to fellow rebels about money contributed to the Correa campaign.
Police found the film on a computer belonging to Adela Perez, a FARC guerrilla captured May 29 in Bogota, a police source told AFP. An official Colombia's prosecutors office confirmed the account.
In the video, dated May 2008, Briceno also talks about compromising documents.
AFP was unable to confirm the authenticity of the video.
Officials with the conservative government of President Alvaro Uribe have long suggested that Correa has links to the FARC.
In Quito, Ecuador's Security Minister Miguel Carvajal dismissed the charges.
"In none of the campaigns has the Pais movement (Correa's political group) received money from the FARC," Carvajal told AFP, adding that the campaign "had no connections" with the Colombian rebels.
Carvajal warned that Colombia has a long history of falsifying information "in an attempt to link the Ecuadoran government with the FARC."
Ties between Ecuador and Colombia have been tense since a March 1, 2008 Colombian military raid that killed 25 FARC rebels at a jungle camp just across the border in Ecuador.
The dead included FARC number two Raul Reyes and an Ecuadoran national.