Liverpool full-back Finnan announced his retirement from international football in January before Trapattoni's appointment, citing the fact that he would be 34 by the time the 2010 World Cup finals come around.
Bolton defender O'Brien, 28, followed suit in February - in a surprise move ahead of the friendly clash with Brazil.
But 21-year-old Manchester City midfielder Ireland's situation is more complicated.
Ireland pulled out of the squad for the European Championship qualifier against the Czech Republic in September.
He initially claimed his maternal grandmother, and then his paternal grandmother, had died, and it later emerged he had lied on both occasions to cover the fact that his girlfriend Jessica had suffered a miscarriage.
Ireland apologised for the embarrassment caused and, although he was called back into Steve Staunton's squad for the clashes with Germany and Cyprus in October, he later pulled out.
Caretaker boss Don Givens did not select him for the game against Brazil in February but Trapattoni is keen to have the talented player back in the fold.
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