The 30-year-old striker has failed to impress since his £5m arrival at the Stadium of Light from Swansea City in 2013, with just one goal in his 39 appearances for the Black Cats.
Graham has proven to be a vital asset scoring six goals in 16 appearances and, with contract on Wearside set to expire this summer, he has refused to rule out a permanent move to Rovers.
Back in April when asked if he would like to stay Graham told the Lancashire Telegraph "yes" but that the decision was out of his hands "at the moment".
He continued, saying Blackburn "took a chance on him" as he wasn't "playing a lot" at Sunderland and had a "tough few years" with "not scoring many goals" which might have "put people off".
Graham said that as soon as he "walked in the door" at Rovers, then manager Paul Lambert knew what he "was about", he could "score goals" and "from the first minute" he said it has been the "perfect fit".
Despite interest from Graham to stay at Blackburn, there is a few bumps in the road in terms of wages and waiting on a replacement for Lambert to be announced.
However the biggest club rumoured with a move for Graham are Scottish champions Celtic, with new manager Brendan Rodgers looking to reunite with his former Swansea City striker at Celtic Park.
It has been rumoured that Rodgers has looked to see if Graham would accept less than his current £35,000 a week wage to move north of the border, with Rodgers looking for reinforcements up front with the likely departure of Carlton Cole and Stefan Scepovic.