The move follows an official dictum from the UK's National Cyber Security Centre warning the Government to remove Kaspersky products from departmental desktops in the interests of national security.
It also requires the ability to communicate back to the company in order to receive updates and share data on what it finds.
Following her warning, Ciaran Martin, chief executive of the NCSC, said Russian Federation had targeted British infrastructure, including power and telecoms.
The letter added that the National Cyber Security Centre is "in discussions with Kaspersky Lab ... about whether we can develop a framework that we and others can independently verify, which would give the Government assurance about the security of their involvement in the wider United Kingdom market".
The guidance continued: "We will be transparent about the outcome of those discussions with Kaspersky Lab and we will adjust our guidance if necessary in the light of any conclusions".
It comes amid rising concerns about Russian meddling in the affairs of Western nations.
"Beyond this relatively small number of systems we see no compelling case at present to extend that advice to the wider public sector, more general enterprises, or individuals", Mr Levy added.
In September, the Department of Homeland Security ordered USA government agencies to remove any products from Kaspersky Lab because of security concerns.
"Whatever you do, don't panic", Levy said.
Eugene Kaspersky, the CEO of the company, told Sky News in October his company had a "strong relationship" with Russian cyber police but they never engaged in espionage activities.
Prime Minister Theresa May said last month that Russian Federation was "weaponizing information" and meddling in elections to undermine the global order.
It has always said there is no truth to the claims. "It's simply not possible".
"It's not true that the Russian state has access to the data".
US authorities are investigating alleged Russian meddling in the 2016 presidential election, and some British lawmakers have called for a similar probe into the U.K.'s European Union membership referendum.