Press Association Sport understands the Football Association of Ireland is in the process of completing the paperwork which will make the former England Under-21 international eligible for selection.
Stearman, who qualifies through his maternal grandparents, has previously spoken of his hope of winning senior international recognition with Ireland.
The 25-year-old told the East Anglian Daily Times in February: ``It's in the process at the moment. I am gaining a passport and citizenship and hopefully that will be not far around the corner.
``All my family on my mother's side are Irish and I am looking to get on the international scene.''
Trapattoni has cast the net wide in recent seasons in an attempt to increase the pool of players from which he can select.
Richard Dunne, John O'Shea, Sean St Ledger and Darren O'Dea have been his central defensive mainstays in recent seasons, but he is keen to blood younger players and Everton full-back Seamus Coleman and Wigan midfielder James McCarthy established themselves as regulars last season.
Stearman's club future is currently uncertain with Ipswich boss Mick McCarthy, who took him on loan from Wolves in January, keen to make the reunion permanent after a successful spell at Portman Road.
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