The sprawling prison, along with its estimated 4,000 inmates, has been caught in the deadly stalemate of Syria's civil war for months.
Rebels have been besieging the facility for the past year, and have repeatedly barreled suicide car bombs into the front gates and clashed with guards and troops holed up inside in an effort to capture the prison.
The Syrian army appears intent on taking opposition-held parts of the country's major cities before the presidential election on June 3.
State-run SANA news agency said army units have regained full control of the town of Heelan, near the Central Prison in Aleppo today and are "advancing toward the surrounding areas after tightening control of the prison."
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Rami Abdurrahman, the director of the Britain-based Syrian Observatory said Assad's forces are positioned about 500 metres away from the complex.
At least 50 rebels have been killed in the shelling, Abdurrahman said.
An activist in Aleppo who works with the Aleppo Media Center told The Associated Press that the government's push to reach the prison complex began yesterday morning.
By mid today, the "regime's tanks have come to about 500 metres away from the (prison) building," said the activist who uses the name Abu Joud al-Mujahid.
There were ferocious clashes between Assad's troops and rebels throughout today, and the opposition fighters are fast retreating from the areas because their weapons are no match for government's superior firepower.
The sprawling prison lies on a highway about 6 kilometres north of the city of Aleppo, once Syria's prized commercial center but now devastated by war, with rebels controlling the eastern part of the city battling Assad's forces controlling the other part.