By Agence France-Presse
"While stressing that the United Nations is not able to independently verify these reports, the secretary-general is conveying his grave concern to the relevant parties," said spokesman Stephane Dujarric.
Ban has asked his envoy Staffan de Mistura to follow up.
"The United Nations underlines the obligation of all parties on the ground to protect civilians and abide by international humanitarian and human rights law," Dujarric said.
"This is particularly the responsibility of the Syrian government and its allies," notably Russia and Iran, he added.
The Syrian army said its military operations to crush the remaining pockets of resistance from opposition fighters in Aleppo were entering the final phase after months of heavy fighting.
About 10,000 Syrians have fled rebel areas in the past 24 hours, mostly to government-held territory, according to the Syrian Observatory of Human Rights.
Last week, the United Nations reported that hundreds of men had gone missing after fleeing the battered city.
The fall of Aleppo would be the worst rebel defeat since Syria's conflict began in 2011, and leave the government in control of the country's five major cities.
More than 300,000 people have been killed since the conflict began in March 2011, and over half the population has been displaced, with millions becoming refugees.
Moscow launched an air war in support of President Bashar al-Assad's forces last year, while Washington has supported rebel forces battling the regime.