The 28-year-old, who joined the Black Cats from Swansea City in January 2013, has been sent out on loan to Hull City and Middlesbrough this season after failing to make an impact at the Stadium of Light.
When asked if he would like to stay with Middlesbrough, he told BBC Sport: "Yes, I would. It's a fantastic club who gave me a chance in football, but I still think I've got unfinished business at Sunderland.
"There's a new manager there now, and I want to go back there in the summer, and see where I stand.
"Until then I don't know what's going to happen, so I've got to get my head down, work hard in the off season, and see what comes of it."
Graham has failed to score in his 13 appearances for Sunderland.