The sources say the militants are located and isolated on one of the upper floors of the complex.
Top Kenyan officials have revealed two or three young American men and a British woman were among the group of attackers who stormed a Nairobi mall killing more than 60 people.
Sporadic gunfire and the sound of blasts can be heard coming from inside the mall.
The details came as dramatic mobile phone footage emerged filmed from within the mall during the attack.
The video shows the chaotic scenes during the Westgate Mall attack allegedly carried out by Somalian terrorist cell al-Shabab, in which 62 people are said to have been killed.
Shoppers crouch behind shelves in terror as bullets are fired inside the shopping centre.
WATCH: FOOTAGE FROM INSIDE THE WESTGATE MALL DURING THE SIEGE
Kenyan Foreign Minister Amina Mohamed, interviewed by US public broadcaster PBS, was asked about reports Americans and Britons were among those to blame for the carnage.
"Yes," Mohamed said. "From the information that we have, two or three Americans, and I think so far I have heard of one Brit."
The Briton was a woman, Mohamed said.
"Woman. Woman. And she has, I think, done this many times before," she told PBS.
"The Americans, from the information we have, are young men, about between maybe 18 and 19," she said, adding they were of Somali or Arab origin but "lived in the US, in Minnesota and one other place."
"So, basically, look, that just was to underline, I think, the global nature of this war that we're fighting," Mohamed added.
Meanwhile, the Kenyan interior ministry announced that troops were "in control" of Nairobi's Westgate shopping mall, with all the hostages trapped by Islamist gunmen believed to have been freed.
A government spokesman told AFP the three-day-long siege, in which the attackers massacred at least 62 shoppers and staff, was close to being declared over. He said special forces combing the building were no longer encountering any resistance.
Somalia's Al Qaeda-linked Shebab insurgents have claimed the attack, which began Saturday, when the gunmen marched into the complex, firing grenades and automatic weapons and sending panicked shoppers scrambling for their lives.
"I think we're all shocked," Mohamed said on the sidelines of a United Nations event in New York.
"And what does it tell us? It tells us that, as governments, we must do better," she said. "If they can cooperate at that level, if they coordinate their evil at that level, that governments around the world must cooperate even more ... to just make sure that we stay ahead of the curve.
"This is a totally new way of doing business for them. And I think we have just seen how much damage can be done," Mohamed said.
Woman 'among the attackers'
The UK's Foreign Office is investigating suggestions a female British terror suspect nicknamed the `White Widow' could have been linked to the terror attack.
Witness accounts have suggested a woman was among the attackers, fuelling speculation Samantha Lewthwaite, who was married to London bomber Jermaine Lindsay, is involved.
She is wanted by Kenyan police over links to a suspected terrorist cell planning bomb attacks.
Six Britons likely dead: London
Full details of those killed in the attacks are yet to emerge, but six Britons are also believed to have been killed, Defence Secretary Philip Hammond said on Monday.
Factbox: All you need to know about al-Shabab
What could have prompted the Nairobi attack?
Earlier: Aussies stories of Nairobi survival emerge
"Our current best estimate is we now have six British nationals who have died in this incident," he said after a meeting of the government's emergency committee chaired by Prime Minister David Cameron.
Three Britons and a dual British-Australian national had earlier been confirmed as among at least 62 people killed in the brutal assault at the Westgate mall in the Kenyan capital.
Hammond said another British victim had been confirmed and officials were awaiting final confirmation on the sixth.
"Of the additional two, one is confirmed and another one we believe to be a British national and we are awaiting final confirmation," he said.
"But we are pretty certain we now have six British nationals who have died."
Referring to the ongoing situation at the mall, where the attack began on Saturday, he said: "It is possible that we will discover further British nationals once the building is fully secured."
British businessman Louis Bawa said his eight-year-old daughter Jennah and wife Zahira were among the dead.
Bawa told the Daily Telegraph that "my heart just stopped" when he was asked to identify them from photographs taken of those killed at the mall.
"The people who did this, they are vigilantes, they are animals," he added.
"They are using religion as an excuse to kill people. Zahira and Jennah were Muslims, but these animals just shot them the same as all of the others."
British press also reported that architect Ross Langdon, who held joint UK and Australian citizenship, died along with his pregnant Dutch partner Elif Yavuz.
Samri Bhamra, from Leicester in central England, said that four members of his family had died while recording an episode of "Junior Masterchef" in the mall, the Times reported.
Cameron cut short a stay with Queen Elizabeth II at her private Balmoral estate in Scotland to return to London on Monday to chair the emergency response committee COBRA.
The committee had held one meeting without him on Monday morning.
