Government forces entered militant-held parts of the Old City late on Tuesday, the so-called British-based Syrian Observatory for Human Rights monitoring group reported, according to Reuters.
A Syrian military source said troops were "advancing in that direction".
The government now appears closer to victory in the city than at any point since 2012, the year after foreign-backed terrorists started wreaking havoc on the country.
The Syrian Foreign Ministry said it would now accept no truce in Aleppo, should any outside parties try to negotiate one. Russia and China vetoed a UN Security Council resolution on Monday calling for a week-long ceasefire. Moscow said rebels used such pauses in the past to reinforce.
The latest developments came after the army took over areas to the east of the Old City including al-Shaar, Marja and Karm al-Qaterji, bringing them closer to cutting off another pocket of rebel control.
Syria has been gripped by civil war since March 2011 with various terrorist groups, including Daesh (also known as ISIS or ISIL), currently controlling parts of it.
According to a report by the Syrian Center for Policy Research, the conflict has claimed the lives of over 470,000 people, injured 1.9 million others, and displaced nearly half of the country’s pre-war population of about 23 million within or beyond its borders.