Carroll has endured an injury-hit second half of the season and is said to have questioned whether playing in the finals in Denmark could do him more harm than good ahead of the new campaign.
Like Wenger, Liverpool boss Kenny Dalglish has suggested he is not in favour of players being drafted back into the under-21 fold after graduating to the senior set-up.
Wenger has also expressed concern about 19-year-old Wilshere suffering burnout as result of the number of games he has played for club and country this season.
Arsene Wenger: "I don't think Stuart Pearce will do it because that is opening the door for any other complaints.
"Players react like that, 'If he doesn't go, why do I go?'
"That could be a dangerous game to leave Carroll behind.
"It could create many other problems.
"I would not be the first on the phone but there would be no logic in the attitude of selection.
"I could understand if Carroll doesn't go for injury problems but for fatigue problems it would be more difficult to convince people in England he is more tired than Jack Wilshere.
"Jack Wilshere is in the red for a while now and this can be a risk for his health.
"He will respect the decision. He knows that he is nearly at the end of his energy level but he is keen to do well.
"He has played nearly 50 games this year. To go to a tournament for me is a massive risk.
"I am happy if the under-21s do well because I want England to do very well.
"I think it is not the right decision but will respect (it) and let him go."