It's unclear what the charges would be, but an announcement is expected Wednesday, the reports say.
The officer, Kim Potter, resigned from the Brooklyn Center Police Department on Tuesday.
Potter fatally shot Wright, a 20-year-old Black man, during a traffic stop on Sunday. Wright's death has sparked nightly protests in the Minneapolis suburb.
Washington County Attorney Pete Orput said Tuesday that he had reviewed evidence in the shooting and expected to file charges Wednesday, according to the Star Tribune.
Sources also told KSTP that charges would be filed. Neither report specified what those charges could be.
While the shooting happened in Hennepin County, the nearby Washington County is handling the case because of the close working relationship between the Brooklyn Center Police Department and Hennepin County.
On Tuesday, both Potter and the Brooklyn Center police chief, Tim Gannon, announced their resignations.
Gannon has said he believed Potter, a 26-year veteran of the force, mistook her handgun for her Taser when she shot Wright.
At a news conference Tuesday, Mayor Mike Elliott of Brooklyn Center said the city was moving toward firing Potter when she quit.
Wright's death has rocked Minneapolis, a city still reeling from the death of another Black man, George Floyd, during an arrest last May.
The officer charged in connection to Floyd's death, Derek Chauvin, is on trial.
Protests in Brooklyn Center turned violent again Tuesday night, as demonstrators surrounded police headquarters, shooting fireworks and throwing objects at officers, according to the Associated Press.
Officers responded by declaring the gathering illegal, 90 minutes before a 10 p.m. curfew went into effect. Officers marched in a line to push the protesters away from the building, the AP reported.
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