Their application has won support from the county's conservation officials, and was to be considered by state wildlife officials on Thursday.
The dead lambs were found in the high grazing areas between Dovre and Sel in Oppland.
The ranchers' leader, Henry Nystuen, told Norwegian Broadcasting that other lambs had to be shot because of serious injuries allegedly inflicted by the wolverines.
Norway has caught international criticism this year for its authorization of several wolf hunts aimed at protecting the country's tradition of open sheep and cattle grazing.
Aftenposten Interactive English Desk
Nina Berglund/NTB