The Crystal Palace youngster has been called up to the England squad for the friendly against Sweden on Wednesday, but is also eligible for Ivory Coast, even if he makes his international debut in Stockholm.
Earlier this week, Zaha claimed that he was torn between playing for the country of his birth or the nation he has represented at several junior levels.
Hodgson hopes that the Eagles forward's promotion to the full squad will act as a motivation for him to pledge his allegiance to England, and has suggested that a lack of commitment could damage Zaha's chances of future selection.
"This is a very simple one for me," he said. "If any player prefers to play for a team other than England they're welcome to do so.
"If the chance to play for our national team is not strong enough motivation for players, they're not type of players we want anyway.
"I automatically - perhaps naively - assume that when I give a chance to a player who has played for the Under-19s and Under-21s I expect him to cycle there if necessary, and not only make himself available but almost thank us for the opportunity."
Zaha has made 17 appearances for Palace this season, scoring four goals.