Dunst and Plemons started dating in mid-2016 after meeting on the set of Fargo. The pair played a married couple, Peggy and Ed Blumquist, on the FX series' second season, which came to a close in December 2015.
"It was a gift," Plemons told reporters at PaleyFest 2015 of working with Dunst.
"I loved Kirsten's work for a long time, and I was really excited once I'd met her, and she's a great person. We're both actors that just ... have fun with the material."
Dunst was spotted wearing a diamond ring Jan. 2 at the Palm International Film Festival, but has yet to confirm the engagement. She was previously engaged to Garrett Hedlund but split from the actor in April 2016.
Dunst will next star in the drama Woodshock with Pilou Asbaek, and is also scheduled for The Beguiled with Elle Fanning. Plemons is slated for Hostiles with Christian Bale and The Discovery with Rooney Mara.