Scott has been absent recently because of health problems.
Costa is the second-highest-ranking Democrat on the committee and has a long history in the ag sector.
He announced his interest Wednesday at a California delegation meeting.
Costa declined to discuss his agenda if he becomes ranking member.
Costa unsuccessfully challenged Scott to be the top Democrat in 2019.
Scott is currently receiving treatment in Georgia for his back and will be absent from House votes until after the members return from Thanksgiving recess on December 3.