Graham has been made available for transfer for Sunderland, with Sam Allardyce keen to offload the 30-year-old.
The former Swansea City man has had a limited amount of action this season, and Allardyce is eager to get the front man off his side's books as he aims to free up room for his intended additions.
Blackburn are said to be willing to make an offer for Graham, but his wages are proving to be an obstacle.
Rovers have breached Financial Fair Play rules in the past, and they are keen not to jeopardise their position again - by spending big on wages.
With Jordan Rhodes already on a sizeable contract, Paul Lambert’s side are not willing to sanction a transfer for another front man, who would be on a similar amount.
As a result, Graham’s switch to Ewood Park is currently in doubt - although a deal still could be completed in the coming weeks, if the striker's wage demands are reduced.