Earlier Nicolas Sarkozy, the French president, had urged the Farc to release Betancourt, saying she was "in danger of imminent death".
No Farc response
Betancourt, a former Colombian presidential candidate, has been held for more than six years.
Al Jazeera correspondent Mariana Sanchez in Bogota says that the Farc has not responded to the offer, nor an earlier offer from the Colombian president to free 500 jailed Farc fighters in exhange for Betancourt.
Farc leader Raul Reyes, left, died in a Colombian
raid in March [AFP]
The group closed lines of communication following the death of one of its senior leaders, Raul Reyes, in a Colombian army raid on a Farc camp in Ecuador on March 1.
Sources in Colombia have reported a doctor was taken to where Betancourt was being held in recent weeks, who later relayed that she was ill both with hepatitis B and a skin disease, our correspondent says.
She was also reported by Colombian intelligence to be very depressed and possibly in need of a blood transfusion, however she has said she does not want to eat or take drugs for treatment, our correspondent adds.
Betancourt is the most prominent of 39 hostages whom the Farc want to exchange with the government for the 500 jailed rebels but the two
sides have so far failed to agree on a deal.
The mission would be accompanied by the International Committee
of the Red Cross, the Colombian leader said after speaking to Sarkozy.
Sarkozy had issued a personal plea to Manuel Marulanda, the leader of the Farc, for Betancourt's release.
"You, who lead the Farc, you have a rendezvous with history. Don't miss it. Free Ingrid Betancourt and the weakest hostages," Sarkozy said.