Browne has been capped for the Boys in Green at youth level, even captaining the Under-19 team, but he has yet to make a senior appearance for his country.
The 21-year-old joined Preston from Cork City in 2014 and has been a regular feature at Deepdale over the course of the past three seasons.
And with Preston challenging for a place in the play-offs in the current campaign, Browne is hopeful that his performances will be enough to impress O'Neill.
"I haven't really thought about it recently but, obviously, it is a long-term goal of mine to break in [to the Ireland squad]," the midfielder said in an interview with Red FM.
"Playing every week [for Preston] is my main ambition at the moment and I think that's what Roy and Martin will be looking for.
"[They'll want] someone to be playing week in, week out and to be playing at a high standard such as the Championship is good for me at such a young age.
"Hopefully, in time, I'll get a chance and, if so, I'll have to take it."
Browne has made 20 appearances for the Lilywhites in all competitions this season. The Cork native played 40 games for the club last term, scoring three goals.