Samantha Lewthwaite, a convert to Islam, was the wife of Jermaine Lindsay and has herself been linked to terrorist activity.
The 29-year-old was wanted by Kenyan police over links to a suspected terrorist cell planning bomb attacks but fled to Somalia in March last year.
Sky News reported seeing a white woman carrying a weapon and wearing a balaclava among the attackers, who have killed scores of people, including four Britons.
A Twitter account claiming to be that of al-Shabaab, the terror group widely believed to be behind the attack, boasted of her involvement.
A tweet from the account, which has since been shut down, said: ‘Sherafiyah lewthwaite aka samantha is a vrave (sic) lady! were (sic) happier to have her in our ranks!’
Lewthwaite, who is originally from Aylesbury, Buckinghamshire, is the daughter of a soldier who became a Muslim after studying for an A-level in religious studies.
A Foreign Office spokesman said: ‘We are aware of the reports and we are looking into them.
‘It is really difficult to substantiate. We are looking at the names and seeing what we can find out.’
The purported al-Shabaab account also named a 24-year-old man from London as one of the gunmen.
The @hsm-press2 account listed a string of names it claimed were involved in the attack before being closed down.
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