The Iraqi forces backed by the US-led air campaign and supported by anti-ISIS armed groups have been able to recapture most of the land occupied by the extremist group.
"The victory announcement will come in a very short time", Prime Minister Haider al-Abadi said on his website Monday evening.
The areas are northwest of the historic Grand al-Nuri Mosque which the militants destroyed last week.
Earlier this month, IS launched a large-scale counterattack in Mosul that underscored the extremist group's resilience in the city despite months of heavy fighting with Iraqi forces backed by USA air power.
Federal police and elite CTS units in Mosul are attacking ISIS fighters in the Old City's maze of alleyways, together with the army and the Interior Ministry's Emergency Response Division.
A US -led worldwide coalition is providing air and ground support in the eight-month-old offensive.
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As a result, these are not "a bunch of misfits nobody wanted", as then-winger Jody Shelley once described the 1992-93 Senators. After that, the team needs to find a captain, a home for its surplus of defencemen and someone to centre the top line.
The militants force women and children to cover them in the streets as they know that Iraqi security forces will not target civilians, he said.
But hundreds of civilians have been killed in the past month as they tried to flee the Old City.
But despite staggering territorial losses, Daesh has managed to launch a number of counterattacks and insurgent assaults inside some Mosul neighborhoods that were retaken from Daesh earlier this month.
Speaking in an exclusive interview with Press TV on Friday, Iraq's federal police chief voiced concerns over Daesh terrorists' use of Mosul residents as human shields.
Islamic State's Baghdadi has left the fighting in Mosul to local commanders and is assumed to be hiding in the Iraqi-Syrian border area.
"The operation is continuing to free the remaining parts of the Old City", Lt. Gen. Abdel-Wahab al-Saadi of the Counter Terrorism Service told a Reuters correspondent near the front line in the heart of the Old City.