Everton midfielder Gibson, who began his absence after missing out on the Ireland squad for Euro 2012, has rejected the opportunity to return to the international fold for the forthcoming 2014 World Cup qualifiers against Sweden and Austria.
Trapattoni told the Irish Times: "I was in touch with him and he said that he is still not ready.
"I saw him in the last game and I told him that I was there but he said that he didn't want the controversy and he wanted to stay so I respect his decision.
"He's a good player and I won't forget him."
Gibson has won 19 caps for Ireland.