Reports claimed over the weekend that Gibson might have to quit Old Trafford to become a regular in Trapattoni's Republic of Ireland side.
The suggestions earned an angry rebuke from Gibson with the midfielder unhappy that Trapattoni was advising him to leave United, stating the Italian 'must have been having a laugh'.
"If Trapattoni wants me to move on from a club like Manchester United to better my game, move to somewhere like Stoke where I'll get more games but have little chance of winning anything, then I just don't know," Gibson told the Derry Journal.
"At what club, other than Manchester United, could I go to improve my game? To be honest, if he's trying to say that I should move somewhere like Stoke City and change my game to winning tackles and not winning games, then he's having a laugh. To move on from Manchester United just doesn't make sense to me."
However, after Ireland's 3-1 win over Andorra, Trapattoni moved to clear up the confusion insisting he never suggested for Gibson to find pastures new, but to work harder to establish himself at United.
"What I told him was that, for him, the action is not finished when he does not have the ball," said Trapattoni.
"I told him that in this great team (United) it is not easy to play in this situation because he plays with ten great players and when these great players have the ball they play.
"He must ask for the ball, he must want the ball. That is important.
"He has to work to get the ball. He has fantastic vision and the long ball and he has a good personality with the ball."