The engaged couple, who began dating in 2016 after co-starring as husband and wife in Fargo, are yet to comment on the reports.
In photos obtained by Perez Hilton, Kirsten could be seen walking in a concealing smock dress in Los Angeles on Tuesday.
No bump sightings just yet!
The publication reports that Kirsten and Jesse are set to wed in Austin next spring, and notes that the actress has already chosen her close pals, Kate and Laura Mulleavy of Rodarte, to create her dress.
Congratulations to the happy couple on their upcoming wedding and the wonderful baby news.