A TRACON Controller reported two aircraft inbound to an airport switched to Tower frequency on their own so the controller could not issue appropriate arrival instructions resulting in a NMAC.

Narrative

Albatros requested a hold over ZZZZZ then VFR practice approach into ZZZ. Citation was about 8 mile southeast of ZZZZZ VFR northbound to ZZZ. The Albatross aircraft started inbound to ZZZ on the practice approach but was not told to contact Tower yet. The Citation started turning towards the Albatross once they were both around 10 miles from the airport. I noticed the turn and the speed difference of the Albatross and the Citation. The Citation was going much faster so I transmitted 'Citation proceed direct ZZZ airport and contact Tower.' I got no response. I tried the same transmission again; no response. I also reached out to the Albatross twice but I did not get a response. The two aircraft were still about 10 miles apart so I proceeded to the give other aircraft traffic advisories; clearances and coordination. When they were about 3 miles apart and 300 ft apart; I started transmitting a traffic alert. No response. A couple minutes later I called the Tower and told them that both aircraft switched frequencies on their own. I told Tower to tell both pilots to not switch on their own. After I got off position; Tower called the facility and reported it was a NMAC.Recommendation: I would recommend the pilots not the switch frequencies on their own. I believe if they would have been on my frequencies the issued could have been resolved.