Wednesday have been tracking Graham for some time, as they feel he could enhance their first-team squad, but Sunderland have been loathed to loan out the front-man to date.
However, after the arrival of Fabio Borini, Graham's first-team chances have been limited and Dick Advocaat is now happy to allow the 30-year-old to leave on a temporary basis.
Advocaat has realised that Graham has little chance of playing regularly at Sunderland, due to their increased depth in the striking positions, and it will now be up to the former Watford man to decide if he wants to move to Hillsborough.
Wednesday have reportedly agreed to pay the entirety of Graham's wages should he join, and they are very keen to get a deal over the line.
Carlos Carvalhal has developed a talented squad at Hillsborough, but they still feel that the addition of a proven goalscorer would strengthen them even further.
At the moment the Owls are sitting in 12th place in the Championship table, but they have won their last three fixtures in all competitions.