Betancourt was abducted in 2002 by Farc fighters in the south of the country as she campaigned for the Colombian presidency.
She is one of 39 hostages that the Farc wants to swap for about 500 of its members in Colombian jails.
Betancourt's family has concerns for her health after videos and pictures emerged of her looking gaunt and in poor health.
Uribe revealed that the Farc offer pertained to Betancourt a day after he first mentioned it.
"Just now the director of the DAS told me she received a call from Farc, in which a Farc individual told her: 'If the president promises, through DAS, not to extradite a Farc member, then they would go ahead with the immediate release of hostages'," Uribe said on Thursday.
|Betancourt has appeared in poor health on |
videos taken during her captivity [AFP]
"I made the pledge. I told them yes, we promise not to extradite this person, but that they should release their hostages," Uribe said.
Luis Carlos Restrepo, Colombia's peace commissioner, received a similar proposal last week, Uribe said.
He said a Farc contact asked Restrepo for a guarantee that Farc members involved in any handover could go into exile.
"The rebels asked if we could guarantee that those who released the hostages would not be taken to jail and if they could immediately go to other countries, like France," Uribe said.
"Our response was positive - 'Free the hostages and simultaneously they can get on an airplane and go to a foreign country'."
Formal neogtiations between the Colombian government and the Farc over the rebel group's hostage are at an impasse.
Two senior Farc commanders have already been extradited to the United States.
The guerrilla group wants them included in any deal to exchange hostages for imprisoned fighters.
But the Farc has been weakened by the recent deaths of three commanders and a series of desertions by Farc members.
To encourage Farc fighters to surrender, Uribe has offered cash bounties, reduced sentences and residency overseas in countries such as France to guerrillas who turn themselves in with any captives they are guarding.
Luis Eladio Perez, a former Farc hostage freed in February, said on Monday that the group would free hostages, possibly including Betancourt, within a week.