SI writer Jim Trotter Trotter said on his twitter account he had been told by a source Harbaugh broke the news to Smith Wednesday.
Harbaugh has made no official announcement, having said earlier in the day he felt the team could win with either quarterback and he would let the situation "play out."
Smith missed last week's game with a concussion and Kaepernick, a rookie out of Nevada-Reno, filled in by completing 16-of-23 passes for 243 yards and two touchdowns in a 32-7 win over Chicago.
The 49ers play in New Orleans Sunday and will take a 7-2-1 record into the contest. Seattle is second to San Francisco in the NFC West with a 6-4 mark.