61.156 says it can be provided by 121 air carrier. From the final rule published in the Federal Register:

To those commenters that suggested the ATP CTP be incorporated into air carrier initial training because the subjects are already taught or because the training only applies to pilots in part 121 operations, the FAA disagrees. The ATP CTP is the base upon which a pilot must build. The concepts in the course will apply to any pilot who flies a large turbine aircraft regardless of operating rule part and therefore has value to pilots flying outside of part 121. The ATP CTP will cover topics the air carrier is not required to teach. For those general knowledge areas that are currently part of a part 121 initial training program, the FAA has modified subpart N to remove those requirements and reduce ground training for those pilots who have completed the ATP CTP. A pilot in an air carrier training program receives training specific to the air carrier’s operation and the specific aircraft that pilot is going to fly. Even if the subjects are offered by an air carrier in initial training, the pilot is focused primarily on learning the company operation and the specific type of aircraft they will fly, not on broader, foundational concepts that the ATP CTP is designed to provide.