He said a unilateral truce declared by the leftist rebels last month "has been a step in the right direction".
The government had previously refused to join the ceasefire, saying the Farc would use it to rearm.
The two sides have been engaged in peace talks in Cuba since November 2012 to try to end decades of conflict.
'Real belief' In a televised address on Wednesday, Mr Santos said peace was closer than ever and it was now time "to de-escalate the intensity of the conflict".
"We're closer than ever to secure peace and make it a reality for us, our children and our children's children.
"I have given instructions to the negotiators to initiate as soon as possible a discussion on the point of the definitive bilateral ceasefire and end of hostilities."
Mr Santos added that high-ranking military officials had already been appointed to manage the process.
Correspondents say up to now the president has been under pressure from the military not to discuss a bilateral truce because of concerns that the Farc would use it to rearm.
But his latest announcement means the government believes the talks are entering into the final stretch, our correspondent adds.
On 20 December the rebels declared an indefinite cessation of hostilities, in an unprecedented move.
Some 220,000 people, most of them civilians, are estimated to have been killed since the Marxist-inspired rebels launched their armed struggle in 1964.
