Pilot reported a NMAC with a MEDEVAC helicopter.

Narrative

I was flying my Mooney M20E. It was approximately XA:15 pm. I was squawking 1200 with Mode C; and ADS-B (out) turned-on. The rotating beacon/strobe light was on. I was approaching ZZZ; from the northwest at about 2;400 ft. MSL (1;300 ft. AGL). Class B airspace overlays this area beginning at 3;000 ft. MSL. I was listening to ZZZ CTAF and heard a Cessna making position reports while making touch and go's; left traffic Runway XX. There was a piece of property I wanted to see that is approximately 6 miles west of ZZZ. I made a visual scan and made a left 360 degree turn at a bank angle varying between 20 and 30 degrees. I straightened out heading east toward ZZZ and reported; 'ZZZ traffic; Mooney; approximately 5 miles west; landing ZZZ.' As I approached ZZZ descended to 2;100 ft. MSL; (Class B airspace begins at 2;400 MSL just east of ZZZ; and pattern altitude is 1;800 ft. MSL.) I again heard the Cessna reporting he was upwind and saw him above the runway. I reported; 'ZZZ traffic; Mooney; two miles west; will cross mid-field; left traffic; full stop XX. I have the Cessna on upwind and; Sir; I will follow you.' The Cessna pilot called; 'Sir we have you in sight; we can extend our upwind and we'll be behind you.' I reported; 'Thank you sir that will work. Mooney is now a half mile west about to cross mid-field; left traffic XX. At that moment I heard on ZZZ CTAF; 'Mooney; MEDEVAC; thank you for flying within 500 ft. of us.' I was configuring my aircraft for landing and extending my landing gear. I immediately reported; ZZZ traffic; Mooney; crossing mid-field; left traffic for XX; MEDEVAC say again?' I again heard; 'Mooney; MEDEVAC; thank you for flying within 500 ft. of us.' I was immediately concerned I had failed to see or hear an aircraft in the pattern and I was in conflict with it. I was on downwind and about to turn left base; I reported; 'ZZZ traffic Mooney; left downwind XX. Sir; I'm sorry. I didn't hear you or see you; where are you?' I heard; 'We were on ZZZ approach south.' It seemed the MEDEVAC was not in the pattern and was somewhere south of ZZZ. I did not hear any other communications from the MEDEVAC. I immediately asked a fellow pilot at the FBO if a MEDEVAC had been at ZZZ. He said no. I don't know what happened. I never saw the MEDEVAC and the other pilot did not communicate where this happened; his heading or altitude. My best guess is that this happened west of ZZZ; either as I flew a 360 degree turn around a property; approximately 6 miles to the west or as I flew east toward ZZZ to land. My radio contact with the MEDEVAC occurred at XA:20 pm. I don't believe I made any violations during this flight. I was diligent and clear of Class B airspace. If the helicopter was below me; I may not have seen it due to ground clutter; or the wing nose or window posts from my airplane. I believe I would have seen the other aircraft if it was above the horizon. I have learned some lessons from this event. 1. MEDEVAC helicopters often transit north to south and south to north; flying west of ZZZ. I should be especially diligent looking for them and other transiting traffic. 2. Be diligent scanning for traffic and making clearing turns while observing property. 3. Monitor ZZZ approach while flying beneath Class B airspace. 4. Turn on the landing light five miles of my destination. 5. I've purchased an ADS-B in capability.