The Swansea City striker is due to undertake a medical with the Black Cats as he finalises a move to the Stadium of Light.
Martin O’Neill has targeted the striker to take some of the goalscoring pressure off Steven Fletcher at the Stadium of Light.
According to reports in Wales . Graham had been holding out for a move to boyhood club Newcastle United after learning of interest from Alan Pardew last week.
But Newcastle are reluctant to pay the asking price and the 27-year-old is expected to complete a switch to his native north-east imminently after Sunderland and Swansea agreed a fee of around £5 million.
Norwich City had also tabled a bid for Graham but the player is not interested in joining Chris Hughton’s team.