ZID Controller observed a conflict on hand-off between aircraft not in communication with ATC which resulted in a NMAC.

Narrative

HTS approach initiated a handoff to me on the VFR a/c. There was merging traffic at the same altitude; not radar identified. I called HTS to make sure they saw and called the traffic. They did not answer the first time I called. The second time I called; the controller answered and said he was not in communication with either aircraft. I noticed the radar identified target merge and climb two hundred feet. I took the handoff when they were clear. A couple minutes later; the aircraft checked on and reported a near miss with Aircraft X; and that he called CRW approach. I reported this to my supervisor. The aircraft canceled flight following shortly after. The HTS called me back again and I told him about the near miss. He said the aircraft may have checked on but he was very busy and didn't respond to him. It sounds like the aircraft went back to CRW approach because he thought he was on the wrong frequency after not getting an answer from HTS. Possibly initiated a call with HTS about the traffic when they were farther apart.