bomber Germaine Lindsay, who blew himself up on a London Underground train on July 7, 2005, killing 26 people.
Media reports, which have dubbed the 29-year-old the "white widow", have linked her to plotting or masterminding attacks across the Horn of Africa region, though with often little clear evidence for her role.
Officials have given contradictory statements.
Kenyan Foreign Minister Amina Mohamed has said a British woman was in the attack, telling the US public broadcaster PBS that "she has, I think, done this many times before."
But Interior Minister Joseph Ole Lenku had earlier denied that any of the insurgents were women, although noting that some male attackers "had dressed like women."
London refused to be drawn Tuesday on Amina Mohamed's comments that a British woman was among the militants behind the mall attack.
A spokesman for the Foreign Office said the ministry was "aware" of Mohamed's comment.
"We continue to liaise very closely with the Kenyan authorities and to support their investigation into this attack," he said.
In 2011 Kenyan police released wanted notices for Lewthwaite saying she was travelling under a false South African passport with the name Natalie Faye Webb accompanied by her three children, a girl and two boys.
The children would be now roughly aged between seven and 12.
Nairobi's Daily Nation newspaper quoted security sources saying that extremists on the Kenyan coast call her "Dada Muzungu" -- white sister in Swahili - - and that she had slipped a Kenyan dragnet in Mombasa in January 2012, when forces raided villas she was believed to have been hiding out in.
"Police have received hundreds of calls from people offering clues and have interviewed dozens who might have met her" in connection with the mall attack, Nairoi's The Standard newspaper said Tuesday, although noting "very few individuals have ever testified to meeting Samantha face-to-face."
Lewthwaite has also been linked to alleged British Islamist militant Jermaine Grant, currently on trial in Kenya's port city Mombasa for possession of explosives.
Grant, who is accused of ties to Somalia's Al-Qaeda-linked Shebab insurgents, was arrested again in December 2011 in the Kenyan port city of Mombasa with various chemicals, batteries and switches, which prosecutors say he planned to use to make explosives.
Rumours abound that Lewthwaite is behind the Twitter handle @MYC_Press -- Kenya's radical Muslim Youth Centre -- which regularly comments on Kenyan extremism, as well as entering into a war of words with rival Islamists.
American Islamist Omar Hammami -- who fought in Somalia but was killed by former Shehab comrades earlier this month -- in April scoffed via Twitter that she was just "a girl in Kenya".
MYC_Press in turn replied: "Sam Lewthwaite thinks ur (you are) a irritating obnoxious contemptible little Muj (mujahedeen) PRAT."
MYC_Press -- which has been notably silent since the attack began on Saturday -- also told AFP in April that Lewthwaite had "returned to Luton", a town outside London and close to where she grew up.