The 27-year-old has failed to make an impact on Wearside following his January switch from Swansea City, but the forward has attracted interest from Hull boss Steve Bruce.
The newly-promoted Premier League side contacted Sunderland within the last 48 hours regarding a loan agreement, according to The Chronicle.
"There's lots and lots of players and it's always wrong for me to talk about them, but [Graham] is someone where there's been a bit of interest," Bruce said.
"He hasn't had the best of times in the north-east but he's a very, very good player. Whether it's possible, who knows? It's something that we're looking at but we haven't done anything just yet."
Reports have claimed that Black Cats manager Paolo Di Canio is open to letting Graham leave the club.