The announcement is set for 11 a.m. in the governor's Statehouse office.
The appointee will fill the vacancy being created by the retirement of Chief Justice Kay McFarland, who was the first woman to serve on the state's highest court.
Sebelius will choose among three finalists whose names were submitted by the Supreme Court Nominating Commission. They are attorney Dan Biles of Overland Park; Douglas County District Judge Robert Fairchild; and Court of Appeals Judge Tom Malone of Wichita.
This will be the fourth Supreme Court appointment by Sebelius, making her the first governor to appoint a majority of the seven-member court since 1960. Before that, justices were elected to the high court.