The newspaper Svenska Dagbladet reports that 24 interpreters submitted a collective application in mid-July. The interpreters are worried that they will be in danger after the international forces withdraw from the country in 2014.
The Swedish Committee for Afghanistan (SCA), working there since 1982, says Afghan civilians serving foreign forces are being killed by opposition movements in southern parts of the country.
"Those who have worked for the International Security Assistance Force, of course, symbolise something that, for many Talibans, is abominable," Torvald Åkesson, general secretary of the SCA, tells Svenska Dagbladet.
Lennart Eriksson at the Migration Board says that while the interpreters association with foreign forces could weigh heavily in favour of their application, Taliban forces are not strong enough in the area to grant asylum for security reasons.
And, he adds, the Migration Board grants neither collective asylum nor preventive asylum ahead of potential persecution.
Migration Minister Tobias Billström told the news agency TT that the government will not grant exceptions to people employed by the Swedish state.
"That would involve changing the legislation, and that is always difficult to do to suit a specific group. An exception or something like it is not being considered," said Billström.