Gibson is happy to come out of exile following the departure of coach Giovanni Trapattoni.
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."