The subject has been identified as 19-year-old Breydale Lewan Campbell, whose last known address was 1506 Darvel Avenue.
Police say Campbell has been known to frequent areas in the Rosehill Road, Shaw Mill Road and Bunce Road areas.
Campbell is only sought for questioning. There are no warrants for his arrest.
The shooting happened near Rosehill Road and Tamarack Drive around 9 p.m. on Oct. 31.
Woods, 19, died after being taken to Cape Fear Valley Medical Center.
Police say he was confronted by two men and shot in the parking lot and then went to a nearby convenience store parking lot for help.
Anyone with information on Campbell's whereabouts is asked to please contact Detective P. Orellano with the Fayetteville Police Department at (910) 988-6543.