Bruce hopes to sign the young Dane on-loan in January.
"If I bring him back, he's going to cost us a lot of money, that's for sure," Bruce told Setanta Sports. "And I would love to bring him back.
"Nick knows he has to show a little bit of patience because sooner or later he will break into the Arsenal team, I am convinced of that.
"But if he became available, of course I would be interested."