Narrative:

At the reported time; aircraft X was switched to my frequency descending via the RNAV STAR out of 7000 feet. I issued a further descent to 4000 feet and a turn from a later fix and queried about their runway preference. The pilot immediately came back and said they had a near midair collision with a C210 at 6500 feet. The pilot was close enough to report the color; make; and markings of the aircraft. The other aircraft was outside of the bravo airspace; running with no transponder or mode C altitude readout. Aircraft X continued on with no further issues.I have already adjusted my radar scope settings to better emphasize primary only targets to avoid missing them in the future. I will ensure that controllers resolve all conflicts before switching an aircraft frequency per the FAA[O] 7110.65 either [by] look[ing] into encompassing the STAR in the class bravo or extending the class bravo to encompass the existing arrival.we should set altitude restrictions on the arrivals and publish them so that VFR aircraft that decide to fly outside the bravo without services know where IFR arrivals will be flying and can plan accordingly.

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Original NASA ASRS Text

Title: Air traffic controller reported a B737 pilot indicated a NMAC had occurred with an unidentified VFR aircraft.

Narrative: At the reported time; Aircraft X was switched to my frequency descending via the RNAV STAR out of 7000 feet. I issued a further descent to 4000 feet and a turn from a later fix and queried about their runway preference. The pilot immediately came back and said they had a NMAC with a C210 at 6500 feet. The pilot was close enough to report the color; make; and markings of the aircraft. The other aircraft was outside of the Bravo airspace; running with no transponder or Mode C altitude readout. Aircraft X continued on with no further issues.I have already adjusted my radar scope settings to better emphasize primary only targets to avoid missing them in the future. I will ensure that controllers resolve all conflicts before switching an aircraft frequency per the FAA[O] 7110.65 either [by] look[ing] into encompassing the STAR in the Class Bravo or extending the Class Bravo to encompass the existing arrival.We should set altitude restrictions on the arrivals and publish them so that VFR aircraft that decide to fly outside the Bravo without services know where IFR arrivals will be flying and can plan accordingly.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.