The Italian tactician has said that the Toffees midfielder must make up his mind as to whether he wishes to play for the Boys in Green or not
The 24-year-old made the decision to withdraw from the Ireland squad ahead of the the upcoming World Cup qualifying match against Kazakhstan, citing disappointment with Euro 2012 as his main reason for doing so, but Trapattoni has hinted that he will not miss the Everton player.
According to the Irish Times, Trapattoni was keen to emphasis the depth of his options at central midfield, naming a number of players who could play in Gibson's absence.
"In the past we were frightened about missing players, but now we already have a squad," Trapattoni told reporters. "He can think about it or we go with other players. We have David Meyler, Marc Wilson, then there is Glenn Whelan, James McCarthy.
"All can play (in midfield), and coming back we also have (Keith) Andrews. When we come here, if there are players who are not coming, we build the other team," he added.
"We have been watching also new players, maybe we will discover a new Irish player. He has to decide whether he wants to play or not," concluded the Italian.
Republic of Ireland face Kazakhstan in Astana on September 7 before hosting Oman in a friendly fixture at Craven Cottage on September 11.