Bruce is looking to bolster his defensive options before the close of the transfer window and has targeted a move for Hull stopper Turner.
Turner's future at Hull has been the subject of speculation this summer with Liverpool credited with an interest in the former Brentford man.
Reports have suggested Sunderland have tabled a £6million bid for Turner and Bruce has admitted he is interested in the 25-year-old.
He said: "It is difficult to talk about individual players. We have registered an interest in the boy [Turner], but that's as far as it's gone as I am aware at the moment."
Bruce is hoping to finally get the green light to seal a deal for Lyon defender John Mensah.
Mensah is poised to join Sunderland on a season-long loan deal and Bruce admits they are waiting on a visa for the Ghana international before Mensah makes the move to the Stadium of Light.
"We are further along with it and we don't envisage a problem," added Bruce. "We are just waiting on the British Embassy in Paris to stamp his visa and once he gets his visa he can get into the country."