SR22
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 7
Human-Machine Interface; Situational Awareness
ATC Issue All Types; Conflict NMAC
Aircraft; Human Factors
I was training an R-side and Aircraft X going to Rockwall (F47) was at 040 and requested lower. Trainee issued 025 and we called to apreq (approval request) with D10. They told us the lowest they could go is 030. I climbed Aircraft X up to 030 and he then reported and aircraft directly underneath him. I scoped in and only saw two aircraft; but neither with traffic for him yet he still said there was an aircraft right under him. I called Approach and asked them if they saw anything and they said they just now were able to see someone. As they said that I finally was able to see the primary target begin to diverge from underneath the target of Aircraft X. After switching the aircraft to D10; I had the CIC (Controller-in-Charge) call the Airport Manager to get the pilot to call us. After speaking with the pilot; he said had I [not] climbed him to 030; he thinks he would have hit the other aircraft and that he may have come to within 125 feet of him.
ZFW Controller reported a NMAC between an aircraft under ZFW Control and a VFR aircraft not under ATC Control.