Skyhawk 172/Cutlass 172
Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 180; Flight Crew Total 1000; Flight Crew Type 1000
Communication Breakdown
Conflict NMAC
Air Traffic Control Separated Traffic
Airspace Structure; Human Factors
C172 departed ZZZ and cleared right turnout to the North. Exited the Class D and tower approved frequency change. Monitored [local] approach. Working with a student; planned to go out a few miles practice climbs; descents; and turns before returning to ZZZ for pattern practice. Heard a traffic advisory to an airliner that an aircraft was 8 NW of ZZZ with altitude (unverified) and direction of flight (that aircraft was us). We did not have the airliner in sight. That was the only advisory given on ATC approach frequency and then that airliner was switched to ZZZ Tower on a visual approach. A few minutes later ATC made a blind call on the approach frequency to our aircraft callsign. We responded and they informed us an airliner was 'rerouted' around us. They gave an updated position of the airliner. The airliner landed without further incident. After completing the flight; had a discussion with tower personnel and they reported that the airliner reported us descending at 400 feet above them at the time being 'rerouted.'
C172 flight instructor reported a NMAC with an air carrier flight.