Wenger has expressed his unease at the 20 year old midfielder's selection in the squad for Wednesday's friendly with Sweden in Stockholm.
"I am aware of Arsene's concerns, which I fully understand as he needs to look after a player who has been out for a length of time," said Hodgson.
"But Jack is an important player for us and now he is fit and playing and available for selection, he understands we are going to put him in the squad.
"He trusts me to make certain I look after him.< p>
"I have made it clear if he plays in this game it will be part of the game and won't be a case of him starting the game and playing 90 minutes, which might be a bit much for him at international level at this moment."
The Three Lions boss added: "Unfortunately, conflict will always exist between national teams and club teams.
"We are never going to get a 100% situation but we are perfectly satisfied."