Reports suggest Assad forces and allies have seized control of 1070 Apartments but armed groups say they are resisting.
The Syrian army says it has taken a strategic district of Aleppo in what would mark the most important advance in the divided city by the government and its allies in weeks.
However, anti-government fighters say the battle is not over.
The 1070 Apartments district is located on the southwestern outskirts of Aleppo and lies alongside the government's corridor into the parts of the city that it controls.
The Syrian Observatory for Human Rights (SOHR), a UK-based group that reports on the war, said government forces and their allies seized full control of 1070 Apartments on Tuesday, calling it the most significant gain by the government in Aleppo since September.