The 28-year-old spent the closing stages of the 2013/14 season on loan at Middlesbrough and could now return to the club where his professional career started.
Gateshead-born forward Graham was picked up by the then Premier League club from Chester-le-Street Town in 2003 and made 15 appearances during a four-year spell.
Graham was loaned out five times during his first stint at The Riverside and two-year spells at Carlisle United, Watford and Swansea followed.
After joining Sunderland in 2013, Graham started last season on loan with Hull City in the Premier League, but when his season-long loan deal was terminated on transfer deadline day in January, the striker joined Middlesbrough until the end of the campaign.
During his time back at Boro, Graham scored six goals in 18 appearances as Aitor Karanka's side finished 12th in the Championship.