The 36-year-old initially called it a day on his Republic of Ireland career in August after his country's disappointing Euro 2012 campaign.
However Given, who has lost his place to Brad Guzan in the Villa side, now wants to be considered for a return to the squad as soon as possible.
"[Giovanni Trapattoni and I] spoke on the phone and I explained why I quit in August and why I am now willing to return," Given told The Irish Sun. "During a lengthy chat, I told Giovanni that I retired because I wanted to concentrate on my club career.
"Obviously, since I made that call, things have not gone as well on the club front as I would have liked or expected, and I haven't started a Premier League game since our second fixture of the season. I knew I was going to miss international football and I suppose that was made worse by the fact that I wasn't playing regularly for Villa.
"So, I began to think about whether I had been too hasty in my choice and started to wonder whether I should reverse it. That's why I felt I had to speak to Giovanni, to tell him how I was feeling and discuss a possible return."
Given is his country's record appearance holder with 125 caps to his name.