Bruce is looking to bring in a new goalkeeper as first-choice Craig Gordon has suffered a broken arm.
The Black Cats also expects Marton Fulop to leave the club in search for regular first-team action.
“James could be somebody that we’re interested in because of the problem with Gordon,” said the Black Cats boss.
“We had had a conversation with David’s representatives and I’ll make my mind up in the next week or so.
“It’s something I didn’t want to happen because I was very happy with Craig Gordon and how he did last year.
“David James has talked to Celtic, which we always knew he was going to do.
“I don’t think he is trying to play one off against the other. He is just keeping his options open at the moment, but we’re still hopeful something will happen.”
