Graham was given an opportunity towards the end of last season and he has been putting in the hours in the gym.
Graham was given an opportunity to impress by Head Coach Dick Advocaat towards the end of last season, and managed to break his scoring duck during a crucial win over Everton en route to avoiding relegation from the Premier League.
The report in the Sunderland Echo suggests that Graham could be a part of Advocaat's plans next season with uncertainty surrounding the future of Steven Fletcher who has a year left on his current contract at the Stadium of Light.
It's a sure sign of commitment from the forward that he is determined to impress and show he can play a role in the side next season, as they will surely look to have their Premier League status secure way before the business end of the season to avoid the nerves of previous years.
In total, the 29-year-old made 14 appearances for the Black Cats last season - and even had a loan spell at Wolverhampton Wanderers while Gus Poyet was in charge earlier on in the season.
Towards the end of last season, Advocaat was happy to play with three forwards so as it stands there certainly seems to be a role for Graham to play at least within the squad - if not the starting XI.
It has been a difficult time for Graham since his £5 million move to Wearside, but after the end of last season, he will be hoping he has done enough to get an opportunity to impress at the start of the new season.