The Canaries shot-stopper has been in inspired form over recent weeks, playing a leading role in Norwich's 10-match unbeaten run.
He has taken full advantage of an unfortunate injury to John Ruddy, with a starting berth in the Premier League falling into his lap.
The former Blackburn Rovers man was already drawing admiring glances from the Ireland set-up prior to earning a regular role, with Sky Sports revealing in September that interest was mounting.
Giovanni Trapattoni is keen to bolster his keeping options after seeing the vastly-experienced Shay Given slip into international retirement.
Bunn is among those under consideration, with the 28-year-old qualifying to represent Ireland through his father and grandmother.