Gould previously worked under Alex Neil when the pair were at Deepdale together.
Neil was in fact the man who brought Gould to Preston back in August 2019.
The Sun, however, state that Sunderland head coach Neil wants to work with Gould again.
Neil has already brought in former Martin Canning as his assistant at the Academy of Light.
Gould, 53, has experience of working in the North East having previously been local rivals Middlesbrough.
During an extensive playing career, Gould turned out for West Brom, Coventry City, Celtic, Preston and Bristol City.
Ex-Sunderland player David Preece was appointed as the club’s first-team goalkeeping coach back in August under Lee Johnson.
Preece, who started his playing career on Wearside, had been working with the Black Cats throughout pre-season and replaced Lee Butler in the role.