Graham was due to train with his new team-mates for the first time today and is likely to be included alongside defenders Carlos Cuellar and Danny Rose, who could return from hamstring injuries.
However, skipper Lee Cattermole will remain on the sidelines after aggravating his knee problem once again on his return to training, while striker Louis Saha has left the club after his contract was cancelled by mutual consent.
Sunderland (from): Mignolet, Westwood, Bardsley, Rose, O'Shea, Kilgallon, Bramble, Cuellar, Mangane, N'Diaye, Gardner, Colback, McClean, Larsson, Johnson, Vaughan, Sessegnon, Fletcher, Graham, Wickham.
Noel Hunt faces a late fitness test ahead of Reading's home meeting with Sunderland in the Barclays Premier League. The striker missed the comeback draw against Chelsea in midweek with an unspecified knock and is again a doubt for manager Brian McDermott. Jason Roberts (hip) will play no part.
McDermott must decide whether or not to promote Adam Le Fondre to the starting line-up. The striker again impressed off the bench against Chelsea, scoring twice for the second successive league game, but McDermott has stressed his best role is presently as a substitute. New signing Nick Blackman is in the squad.
Reading (from): Federici, Taylor, Gunter, Kelly, Cummings, Pearce, Morrison, Mariappa, Shorey, Harte, McAnuff, Carrico, Tabb, Karacan, Kebe, McCleary, Robson-Kanu, Leigertwood, Le Fondre, Hunt, Pogrebnyak, Akpan, Blackman.