Moyes, named as Sir Alex Ferguson's successor at Old Trafford on Thursday, would take questions only about Sunday's Premier League game against West Ham, the club said.
Everton said Moyes would hold a media conference at 12:30 GMT but added in a statement: "Please note Mr Moyes will not be answering any questions on the subject of Manchester United or his appointment as the club's new manager."
Sixth-placed Everton play mid-table West Ham at Goodison Park on Sunday before facing Chelsea in their last game of the season at Stamford Bridge on May 19.
Moyes officially takes over at United on July 1 after Ferguson, Britain's longest-serving and most successful football manager, announced on Wednesday that he would retire.
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