Clark's challenge to beat Arsenal's unbeaten record came to a halt at The Valley this week, but he is tipped to be a Premiership manager of the future.
Clark is a Geordie and he would never consider another move to the Stadium Of Light.
Former Aston Villa boss O'Neill and Mark Hughes were swiftly installed at the top of the bookmakers' lists.
Bruce's assistant Eric Black will take charge of the side for Sunday's trip to Wolves, but former chairman, Niall Quinn would like O'Neill appointed as soon as possible.
O'Neill has been out of the game since leaving Villa in August last year, but has been linked with virtually every managerial vacancy since.