Santos, the former defence minister, won Colombia's run-offpresidential election last month.
He promised to continue the policies of Alvaro Uribe, the outgoing president, who was unable to run for re-election after a constitutional court barred him from seeking a third term.
Al Jazeera's Teresa Bo said that the release of the video, the authenticity of which could not be verified, came at a crucial time for the country.
"This is happening only days before the elected president of Colombia, Juan Manos Santos, who will succeed president Alvaro Uribe, takes office. This is no coincidence," our correspondent said.
"He is also sending a message to Juan Manuel Santos about the future and what he should do."
In the video, Cano also said that the new president has merely undertaken a task "of rearranging a political regime".
"[This government] is filled with illegitimacy because it has been taken over by drug trafficking, by administrative corruption, and impunity."
"The whole electoral apparatus is rotten. It is characterised by terrorist violence in a substantial way."
Uribe's two four-year terms in office were marred by scandals over corruption and human rights abuses, including arrests of legislators for "colluding with death squads" and a probe into state spies illegally wiretapping journalists and judges.
But he remains popular for battling the Farc fighters, using billions of dollars in US aid to push them away from Colombia's main cities.
The Farc fighters have said that they will keep up their fight against the government.
"People can vote for whom the want, but we will continue fighting," Commander Duber of Farc told Al Jazeera on the eve of the election.
"The ideology of the Farc is to win or die, that's what Che Guevara said."