A government offensive to retake all of Aleppo has pounded the city in recent days.
"The Russian Federation announced that... they want to sit down in Aleppo with our people there to discuss how we can use the four corridors to evacuate people out," Jan Egeland, head of the UN-backed humanitarian task force for Syria, told reporters in Geneva.
"We have at least 400 wounded that need immediate medical evacuation," Egeland said, adding that there would also be discussions on using "these corridors to get medical supplies and food in."
His comments came as hundreds of elite Syrian troops were moving into east Aleppo Thursday ahead of a push into the most densely populated areas, after the UN warned the city risked becoming a "giant graveyard".
A government offensive to retake all of Aleppo has pounded the city in recent days, with the relentless barrage leaving Aleppo's streets strewn with the bodies of men, women and children, many lying next to the suitcases they had packed to escape.
The Syrian Observatory for Human Rights, a monitoring group, said Wednesday that more than 50,000 people have fled Aleppo's rebel-held districts to both government-held territory and Kurdish-controlled districts.
Egeland, who put the exodus at at least 27,000, said the UN had access to all the people in both the government- and Kurdish-held areas, but still could not reach those in besieged parts of the east.
Syria's main ally Russia has previously unilaterally declared the creation of evacuation passages from east Aleppo, but the UN was not involved and the routes, which came under rebel fire, went largely unused.
Egeland acknowledged that previous attempts at setting up humanitarian corridors had not been successful due to "issues with both sides," but said "a humanitarian corridor can work if all the armed actors respect it".
He said Russia has pledged to respect the corridors, and that "we (the UN) now feel confident that the armed opposition groups will do the same".
"Now I think it has dawned upon all sides the urgency of the situation," he said.
The UN peace envoy for Syria, Staffan de Mistura, told reporters that a humanitarian "pause" in the fighting remained UN priority.
Egeland said access to the besieged areas of east Aleppo was essential, adding that the UN has enough food stored in western Aleppo to feed 150,000 people in the east, as well as medical supplies to cover all the needs there.
As for western Aleppo, he said the main concern was providing adequate shelter for those flooding in from the east, who are joining some 400,000 displaced Syrians already in that part of the city.