The 27-year-old, who joined the Black Cats from Swansea City in January, has just returned from the club's pre-season tour of Italy ahead of finalising a move.
Having seen a move for Charlie Austin fall through last week, it is now thought that the Tigers are eager on completing the signing of Graham.
Manager Steve Bruce admitted earlier this week: "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.
"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."
Graham is yet to score for Sunderland, having made 13 appearances since his £5m from Swansea.