The radio station said that Erman was likely to be confirmed as finance minister by parliament in early September. The prime minister's cabinet was not available for an immediate comment. Erman would replace Dusan Mramor who resigned in July, citing personal reasons.
Erman, 50, who is a legal expert by profession, has worked at the ministry of finance since 1993 and has been a state secretary for the past six years, dealing mainly with taxes and the budget. She is not politically affiliated.
"We have to wait and see whether the fact that she is not politically affiliated will be positive, as she will not have to worry about her future political career, or not," Saso Stanovnik, chief economist at investment firm Alta Invest, told Reuters.
Erman's main task will be to reconcile demands for public sector wage and pension hikes with the need to further reduce the budget deficit which last year fell to below 3 percent of GDP, as required of EU members, for the first time in seven years.
The government had said it plans to cut the deficit to zero by the end of 2020.
"Further deficit cuts will largely depend on whether the government coalition continues to support fiscal consolidation amid improved economic conditions," Stanovnik said.
Slovenia, which narrowly avoided an international bailout for its banks in 2013, returned to growth in 2014 and expects its export-oriented economy to expand by 1.7 percent this year versus 2.9 percent in 2015.