In the family drama directed by Joachim Trier, Skarsgård plays the director Gustav who tries to repair his relationship with his two adult daughters.
The film is also on the list for best cinematography and in the new category of best cast.
Swedish composer Ludwig Göransson has a chance to expand his Oscar collection – partly for the music for the film "Sinners" but also for two songs from the same film.
However, the Oscar journey ended before it had begun in earnest for the Swedish entry in the Best Foreign Language Film category, Tarik Saleh's "Eagles of the Republic".
The final nominees will be revealed on January 22. The Oscars will be held on Sunday, March 15.
