A Center Controller reported they observed an unidentified target with no transponder in their airspace. A B737 in the vicinity reported they observed the target in that area.

Narrative

A Mode C Intruder target appeared on my radar 9 miles west of the ZZZ Airport. It showed an altitude of 28800 ft. I did not have any idea who or what the aircraft was or whether or not there really was an aircraft there. I called the traffic to an ZZZ1 arrival; a Boeing 737; and they reported that they had the traffic in sight. This greatly concerned me because that meant that this target wasn't some radar anomaly or an aircraft's transponder malfunctioning. This was visual confirmation from a professional pilot that yes; something indeed was up there at 28800 ft. I asked the pilot to describe the size of what he saw; asking him if it was bigger or smaller than his aircraft. He reported that it was about the same size as his Boeing 737. This is an incredibly dangerous situation and one that should be gotten to the bottom of. This is not the first time that unidentified targets have been seen in our airspace. Nor is it the first time these targets have been corroborated with a visual sighting. I quickly reported the situation to the Controller In Charge who then reported it to facility management. Just as in the last time this has happened; I fear that nothing will either be done in coordination with the controllers; whose job it is to separate traffic; or at all. Investigate these reports seriously. This is a safety issue more than anything.