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Published 10:46 5 Sept 2016 BST
Updated 12:05 5 Sept 2016 BST
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Mike Phelan has been the caretaker manager since Bruce's departure at the end of July, and widely expected to take the role on a permanent basis.
O'Neill's last Premier League managerial role was with Sunderland between 2011 and 2013.
The 64-year-old was dismissed with seven games remaining in the season and replaced by Paolo di Canio, with the club one point above the relegation zone.
There were no suggestions that O'Neill is looking to walk away from his role with Ireland at the press conference ahead of Monday's game in Belgrade.
"I don't see why not. I've enjoyed this immensely," O'Neill said when asked if he would turn down an approach from a Premier League club.
"The qualification group was tough and the games were gruelling and to get to France and experience all that there was amazing.
"Who knows what might happen in the future? But I really do genuinely enjoy it."

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