The Black Cats have confirmed that Reid has resumed running in the latest stage of his rehabilitation.
The 27-year-old missed the last three months of the season with a troublesome calf injury but is now aiming to be fully fit for the start of pre-season training.
A series of niggling injuries restricted the Republic of Ireland international to just 20 Premier League appearances last season and he did not feature after the 1-1 draw with Portsmouth on February 9.
Goalkeeper Craig Gordon is also making steady progress on the road to recovery after having a metal plate removed from his arm.
The Scotland international fractured his arm against Tottenham last November and returned to action in January after having the plate inserted.