"Keiren clearly wants to play some games, of course he does. The fact is I'm very reluctant to let anyone go because we simply don't have the back-up," said O'Neill.
Given hinted last month that he would consider ending his international retirement and make a return to the squad, but the 36-year-old has had no contact with Trapattoni.
"I haven't decided yet," Given said ahead of tonight's League Cup semi-final clash with Bradford City where he'll make a rare appearance for Aston Villa.
"I haven't spoken to the Ireland manager, I want to speak to him before I make any announcements."