Commander 112 Pilot reported NMAC with another aircraft in cruise flight.

Narrative

After completing a touch and go at ZZZ and maintaining my discrete transponder code; I was given a left turn to 190 degrees and Tower verified I desired flight following for maneuvering south of ZZZ1. I affirmed my desire for flight following. When I was over downtown ZZZ; Tower advised me to contact ZZZ Departure. I checked in with Departure (with current altitude climbing to 3000 ft. heading 190) to which they responded with radar contact and gave me an 'on course' to the east and 'altitude my discretion'. I confirmed this and continued my climb to 3000 ft; proceeding on a 090 to 100 heading. At or about XA:10; ATC told me there was traffic at my 12 o'clock X miles (I believe they said 3 miles but I'm not sure; it was close whatever they said); 'type and altitude unknown'.As it was clear this was a primary radar target; I was not really sure what I was looking for; I assumed an aircraft. I scanned directly ahead and left and right; being sure to look around my side window frame forward posts. I did not see anything visually nor was anything on my ADS-B which was expected due to ATC not talking to anyone and they had no idea of the 'aircraft' type. I flew on for another minute or so; constantly looking ahead and to each side. When I looked back to the left; I caught the sight of an aircraft tail going beneath me. I turned to the right to see the aircraft continue in level flight in the general direction of ZZZ2. They were not executing any maneuvers other than straight and level. There were no radio calls from the aircraft. I'm not sure if he/she even saw me. I noted my altitude was 3200 indicated. I must have instinctively climbed having seen the aircraft below. I estimate the aircraft was approximately 200 ft. below me; though I initially broadcasted to ATC that the aircraft was 500 ft. below. It was much closer because I remember seeing the gas caps. The aircraft was mostly white with red trim and appeared to be a C172 like aircraft. I do not recall seeing any beacons or NAV lights. ATC asked what altitude the aircraft was at. I told them 3000 ft. I later heard the Controller tell another aircraft of the unidentified aircraft at my estimated altitude. I continued the flight without further events. Not sure what else I could have done.