The Blackburn native has been capped for Ireland at Under-21 level but still has the option to play for England at senior level.
Trapattoni says he is excited to see what the 24-year-old can do in an Ireland shirt.
"I can say with certainty that he is very interested to play for us," the 73-year-old told the Irish Examiner.
"He is honoured with the interest and the paperwork is being processed at the moment. Who knows, we might be able to see him in early February."
"He is a very particular type of player. He is technically excellent and he is very physical.
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The Italian is eager to integrate Pilkington into his squad because of his versatility and technical ability.
He added: "I don’t know if during my time here we have had that type of player, who is at ease both on the left and right wing, and who can come in and create difficulties for defences.
"I think he is also a great threat in front of goal. There are a lot of different ways he can attack in the air. He has a great strike of the ball and he is not afraid to take a shot.
"He is excellent at set-pieces, his physical and technical attributes are there for everyone to see. He is a bit different from Duff, Lawrence, Hunt and even McClean. He is able to offer a lot in different areas of the pitch."