Bunn was born in London but qualifies through his father and grandmother.
Bunn, 28, said: "It's one of my aims now to try and break into the Republic squad and if the chance arose I'd definitely be interested.
"Every player wants to play international football and play at the highest level and I'm no different.
"I believe the goalkeeping spot with the Republic is up for grabs since Shay Given retired.
"But I now have a run of games in the Norwich team and it is a good chance for me to show what I can do and hopefully impress."