It's a gem of a left foot, as he also demonstrated against Waterford earlier this year.
Burke has been in scintillating form for the Dublin club this season and is joint top scorer in the SSE Airtricity League Premier Division with nine goals.
"He has nice ability", O'Neill said.
Bradley said: "We are in the middle of the second series of league games when the global games come around so I will be speaking with Martin [O'Neill] on how we can best accommodate each other and hopefully we see Graham wear the Ireland jersey soon enough".
"From that viewpoint it's good, and it's nice to have him in the squad".
O'Neill announced his provisional squad at the SPAR FAI Leinster Primary 5's in Navan this afternoon, and along with Burke, it includes three other "first-timers".
O'Neill also feels that the upcoming games are chance for some new talent to shine. League of Ireland players receiving global call-ups is something of a rarity, but the former Aston Villa man has been on fire this year and gets the nod up front along with fellow new recruit Callum Robinson of Preston.
"It was his overall play and I think he did really fine in the game".
"The year that Forest won the championship, we were flying and playing in European football for the next couple of years". I don't really know what more you have to do to get a bit of recognition.
"And I think, why not?" I have, during my time, put some players into the squad that have made a peripheral squad and then dropped out.
"That would be my advice to him, if he gets on the field of play in this match, just go and play your game, go and play". I can't say easy, but they came easier to me in that sense.
Expect that squad to be cut down significantly, especially after the Celtic match when every player above will be available.
"I just want to clarify that, he will be involved in the Celtic game".