The Houston Chronicle reported that indicates Kubiak will be keeping his job for a sixth season.
Bush had been the Texans' top defensive coach for two seasons. Team owner Bob McNair wants Kubiak to hire a well-known coach with a proven track record in the mold of Wade Phillips, the newspaper said.
Texas finished its 2010 season with a 6-10 record. Kubiak is 37-43 in five seasons.