B737-900
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (mon) 6; Air Traffic Control Time Certified In Pos 1 (yrs) 6
Situational Awareness; Workload; Communication Breakdown; Distraction; Human-Machine Interface
ATC Issue All Types; Conflict NMAC
Flight Crew Requested ATC Assistance / Clarification; Flight Crew Took Evasive Action
Weather; Human Factors; Company Policy; ATC Equipment / Nav Facility / Buildings; Airspace Structure
Working combined feeder sectors; typical arrival traffic; not busy but not slow. Aircraft X was arriving ZZZ1 via the ZZZZZ arrival and had been issued a descent to 8;000 feet as is normal for an aircraft in their position.  Suddenly; Aircraft X announced that they had to level off because they had almost hit what they were describing as a Aircraft Y that was skimming along the tops of the cloud layer at approximately 10;000 feet.  I had not previously observed traffic in the vicinity of Aircraft X; but upon their comment I did observe a primary only target emerging just east and behind ASA's radar target.  I informed the supervisor of the event and subsequently issued the information to Center; because the primary target appeared to be continuing into their airspace and there were other aircraft inbound from that direction.Had I observed the primary target converging with Aircraft X; I would like to think that I would have issued the traffic regardless of the fact that it was only a primary return.  Issuing traffic would likely have not prevented the incident; because even with traffic issued I would not have altered the descent instructions.  However; traffic being issued would undoubtedly have prepared the crew more appropriately. It is also worth mentioning that we observe false targets in our airspace on a relatively regular basis.  I would be naïve to assert that it is possible to issue traffic on every primary target to every aircraft 100% of the time.  Particularly given that I was working both the feeder sectors combined; which essentially means my scan is the entirety of our airspace.  Had the feeder sectors been split; there is an additional possibility that my scan would have caught the primary target and I would have issued traffic.Additionally; while I believe the primary target was technically just outside of the Mode-C/ADS-B Out veil around ZZZ1 at the location that the incident occurred  my guess is that the aircraft departed from a satellite airport underneath that veil (even if just barely).  To my knowledge no aircraft contacted the facility today to inform us of their intentions to operate in the vicinity of this incident without Mode-C/ADS-B Out capabilities.  So; the aircraft's compliance with applicable regulations pertaining to their equipment may have averted this incident as well.
A TRACON Controller reported an air carrier pilot reported an NMAC with an unidentified VFR aircraft that was not displaying a transponder or in communication with ATC.