The increase from Berlin's current cap of 4,500 would be put before parliament in December when the mandate for the mission comes up for renewal, the report said. All but one of the main parties in parliament have supported the mission until now.
Deutschlandfunk, which did not cite the source of its information, said that Berlin wanted the increase to give Germany greater clout at an upcoming international conference on the increasingly bloody eight-year-old mission.
The conference, which Chancellor Angela Merkel wants to use to press the Afghan government to assume more responsibilities, will take place in February or March, and not later this year as previously expected, the report added.
Last year press reports said that Berlin wanted to raise the upper limit to 4,500 troops from 3,000. Initially denied by the government, the reports turned out to be accurate.
The German contingent, the third-biggest in a 100,000-strong international force including 65,000 under NATO command, is based in the relatively peaceful north of the country, which has become more violent in recent months.
A spokesman for the Defence Ministry called the radio report "pure speculation," highlighting that Merkel, fresh from her election victory on Sunday, was still working a common programme with her new coalition partners.
A spokeswoman for the Foreign Ministry said only that a "new mandate was something for the new government and for the new parliament."
Opinion polls show that the mission in Afghanistan, which has seen German soldiers' heaviest fighting since World War II, is highly unpopular. Thirty-five German troops have been killed since the deployment began in 2001.
The commander of international forces in Afghanistan, US General Stanley McChrystal, has warned in a leaked report that the conflict could be lost within a year without more troops.
McChrystal has asked US President Barack Obama to send another 40,000
soldiers as part of a rigorous counter-insurgency push. The White House says Obama will only decide on whether to accept the general's request after first arriving at a new US strategy, a process which officials say could take weeks.