The ICRC received a green light from Syrian authorities on Thursday, hours after opposition forces left the heavily bombarded area following a 26-day siege aimed at crushing a symbol of the revolt against President Bashar al-Assad.
"We are in Homs preparing to enter Baba Amro," ICRC chief spokeswoman Carla Haddad told Reuters in Geneva at 1100 GMT.
With government forces moving in, the UN human rights office voiced alarm over reports suggesting former opposition areas were being subjected to reprisals.
"We are alarmed at reports starting to come out of the Baba Amro district of Homs after it was taken over by government forces yesterday (Thursday)," UN human rights spokesman Rupert Colville told a news briefing in Geneva.
"Although we are not, at this point, in a position to confirm any of those reports, we would like to remind the authorities of their responsibilities under international law.
"It is essential that there are no unlawful reprisals, no summary executions, no torture, no arbitrary detention. And the rights of those who are detained must be respected," he said.
As opposition fighters withdrew from Baba Amro, the opposition Syrian National Council (SNC) warned of a "massacre" in the district.
Activists said Syria's army had begun hunting down and killing insurgents who had stayed to cover their comrades "tactical retreat," although the reports could not be verified.
ICRC spokesman Hicham Hassan said the ICRC convoy consisting of seven truckloads of food and other aid had left Damascus on Friday morning bound for Homs, but snow had slowed its course.
"Red Crescent volunteers and ambulances are waiting in Homs for the convoy to arrive and we are hoping to enter Baba Amro as soon as possible," he said.
Over the past week, ambulances of the Syrian Arab Red Crescent evacuated 30 people from Baba Amro, taking the most seriously wounded to hospitals in Homs.
The ICRC has said that it does not know how many sick or wounded may need medical attention or evacuation from Baba Amro.
The independent agency is the only one to deploy aid workers in Syria, where the United Nations has been shut out.
Russia and China joined other UN Security Council members on Thursday in expressing "deep disappointment" at Syria's failure to allow the UN humanitarian aid chief Valerie Amos to visit the country and urged that she be allowed in immediately.
UN human rights chief Navi Pillay, speaking to the UN Human Rights Council in Geneva on Friday, said: "The escalation of violence in Syria is of utmost concern. The international community has an urgent responsibility to act to bring an end to the heavy loss of life in Syria."