The former Swansea striker has returned from Sunderland's pre-season tour of Italy.
He has not scored a goal for Sunderland in 13 appearances since his £5m move to the Stadium of Light in January.
Bruce, who saw a move for Burnley's Charlie Austin fall through, admitted his interest in Graham 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 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."