The 28-year-old is on a good run of form under Chris Hughton with the Canaries.
But despite pledging his allegiance to the Republic earlier this season - Bunn qualifies for Ireland as his paternal grandmother is from Co Kildare - the call has yet to come from Giovanni Trapattoni.
With Keiren Westwood starved of first-team football at Sunderland, Forde has managed to establish himself as first-choice with Ireland but Bunn is desperate to change that and join Canaries team-mate Wes Hoolahan in the squad.
"It was disappointing not to make the squad for the last two games, but all I can do is continue to do my best for Norwich and hope I get a call-up next time," said Bunn.
"I have a very strong Irish connection. My dad's mum is from Maynooth, my dad considers himself Irish and so do I," he added.
"I know it would mean a lot to my grandmother to see me play for Ireland.
"She always talks about it and she's always hoped that her grandson could play for the Irish team."