The Home Office is considering whether to ban BNP members from working in the civil service.
The BNP has said bans on membership are 'anti-democratic'
Martin Narey, the government's diversity champion, is working on the issue but no decision has been taken.
The Home Office emphasised the matter had not been discussed with ministers. Civil service chiefs themselves are also not currently considering a ban.
The Association of Chief Police Officers recently decided officers could not be BNP members.
The British National Party has done well in recent elections, and says it is wrong to stop people from being members of a legal political party. The party denies it is racist.
Former anti-apartheid activist and Commons leader Peter Hain described the BNP as a "vile party of Nazis and thugs" and suggested last week that its members were not fit for office.
In November last year, Home Secretary David Blunkett backed a ban on police officers being BNP members, and chief constables agreed the measure two months ago.
The Sunday Times reported that civil service unions had already been consulted over a ban.
It quoted Charles Cochrane, secretary of the Council of Civil Service Unions which represents 400,000 workers, as saying there was an "inescapable logic" behind a ban.
"There isn't any fundamental legal obstacle to this."
But it is understood that new legislation might be needed to enforce a ban.
The BNP has said bans on membership are "anti-democratic" and could challenge any proscription using the Human Rights Act.
But if brought in, the civil service would argue, like the police have, that being a member breaches rules on diversity.
BNP spokesman Phil Edwards told the Sunday Times: "This is totalitarianism, Soviet-style. It shows they are extremely worried."