The Republic of Ireland boss confirms he has given the Latics playmaker the day off to decide his future, with Everton interested in signing him.
The Toffees are interested in signing the Wigan playmaker as a replacement for Marouane Fellaini, who appears bound for Manchester United.
Trapattoni, whose Ireland side faces Sweden on Friday, admits he has given the 22-year-old the day off to settle where he will be playing his football this season.
"I spoke with James McCarthy, he has the opportunity to change team," Trapattoni told reporters. "I told him to stay with the club now to decide your position because he could be happy, because of the new possibility will be for him very important.
"Also, one day more for us [is no big deal] it would be very important, also important that he comes back happy after this situation."
McCarthy could become the third Wigan player to move to Goodison Park this summer, reuniting with former boss Roberto Martinez and teammates Antolin Alcaraz and Arouna Kone.