The 25-year-old Everton midfielder has made himself unavailable for his country since returning from the Euro 2012 finals without kicking a ball.
However, the 74-year-old Italian's departure has prompted Gibson to offer his services once again amid the ongoing search for Trapattoni's successor.
Asked about the timing of his decision, he told the Irish Times: "Obviously because Trapattoni is gone.
"I never really wanted to make a big deal of it to be honest with you. But after what happened at the Euros, I just felt I couldn't play under him anymore.
"I was embarrassed when I came back from the Euros [after] not winning a game and not getting on the pitch.
"I was playing every week at the time for Everton and we finished in the top six of the Premier League.
"Obviously I didn't get on and I just felt he had some sort of problem with me - but I felt he had a problem with me before the Euros as well as I never played.
"Like I said, I didn't want to make a big deal about not playing under him, so I kept myself quiet. But I am available to come back now."