A Center Controller reported an aircraft flying an approach to a non-towered airport reported a NMAC with a departing aircraft.

Narrative

Aircraft X is doing multiple test approaches at ZZZ while VFR. They were not on the frequency best served at the ZZZ airport but the other frequency that sector has. While Aircraft X was conducting an approach; a VFR target departed ZZZ heading directly into the Aircraft X path. When ERAM conflict alert went off I could read the tail number of the VFR aircraft. At this point I made a traffic alert call to Aircraft X about the VFR target with no response; the targets merged and had only about 100 feet between targets. I then relay through another aircraft to change the Aircraft X frequency. Once Aircraft X got on to [frequency] I was able to give additional advisories to them. Aircraft X advised me that this other aircraft was not on the CTAF either. It appeared that this VFR target (Aircraft Y) was intentionally flying at the Aircraft X. Aircraft X did give me the tail number of this VFR target and when questioned; the Aircraft X said they needed to make multiple maneuvers to avoid a mid-air collision. Aircraft X wanted to report dangerous activities from Aircraft Y.A previous controller needed to ensure that the Aircraft X was on a frequency best suited for their operations at ZZZ. Otherwise this looks like dangerous behavior from a pilot that was not in communications with ATC nor on the ZZZ advisory frequency.