Bruce is keen to bolster his attacking options ahead of the new Premier League campaign, having seen a deal for Burnley striker Charlie Austin fall through due to a failed medical.
Reports on Tuesday claim the Hull boss has turned his attention to Graham, with Sunderland believed to be willing to let the forward go just six months after his £5million switch from Swansea.
Bruce claims Graham is a "very good player" and is reported to be keen on a season-long loan for the 27-year-old.
"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 told the Hull Daily Mail.
"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."
Steve Harper is one player who Bruce has managed to get on board, and the former Newcastle goalkeeper is delighted to have moved down the east coast.
"I really enjoyed training today it was fresh and new and exciting. It was perhaps something I should have done years ago," he told Sky Sports News.