Canadian Brigadier General Dave Anderson, who oversees the training of local forces for the US-led coalition, said Iraqi security forces have pushed IS into a final, small pocket of Mosul's Old City by the Tigris River.
An Iraqi broadcaster announced: "It's a matter of hours".
Backed by a ferocious aerial bombing campaign by a US-led global coalition, the offensive has turned much of the city to rubble and forced tens of thousands of people to flee.
Nearly exactly three years ago, the ultra-hardline group's leader Abu Bakr al-Baghdadi declared from Mosul a "caliphate" over adjoining parts of Iraq and Syria.
Isis fighters are putting up a fierce resistances with suicide bombers, snipers and grenades, hampering the progress of Iraqi troops.
"The battle has reached the phase of chasing the insurgents in remaining blocks", the Iraqi military media office said.
"We have a tip-off that besieged Daesh militants in the Old City were planning to storm eastern Mosul and cause chaos in some liberated areas", Mohamed told Anadolu Agency.
The jihadists wanted to go back, but security forces "fired on them and killed them", he said, without specifying how many died.
Prime Minister Haider al-Abadi declared the end of Islamic State's "state of falsehood" a week ago, after security forces took Mosul's medieval Grand al-Nuri mosque - although only after retreating militants blew it up. The militants are expected to keep up attacks on selected targets across Iraq.
Earlier, a top United Nations official for Iraq's affairs said more than $1 billion would be needed to reconstruct the city following its liberation.
In Mosul on Saturday, jubilant interior ministry forces - whose mission has been declared over - were seen flashing V-for-victory signs and posing for selfies in front of each other holding up IS's notorious black flag upside down. Iraq's regional Kurdish leader said the Baghdad central government had failed to prepare a post-battle political, security and governance plan.