The Toffees are interested in signing the Wigan playmaker as a replacement for Marouane Fellaini, who appears bound for Manchester United after the two clubs agreed a £24 million fee.
|20/1||Everton are 20/1 with BetVictor to finish in the top four 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 team-mates Antolin Alcaraz and Arouna Kone.