The England manager, who gave the Old Trafford-bound forward his first international cap in November, expects the youngster to get and take his chances with the Red Devils.
The Three Lions boss gave the youngster, who will play his last game for Crystal Palace in the Championship playoff final on Monday, his first senior cap in a friendly against Sweden in November, and he will join the reigning Premier League champion for next season after signing for Manchester United in the winter transfer window.
"I like Wilfried Zaha. He is a good player," Hodgson told the FA's official website. "I went to Palace not so long back to have a look at him and, of course, he has a massive move to Manchester United. It seems to me he is on the threshold of something big."
Though he cannot control how much playing time the forward will receive next season at Old Trafford, Hodgson expects him to impress.
"He will be given the opportunity," Hodgson said. "When a club like Manchester United is prepared to pay a lot of money for a player because they will help them to win things it is a tremendous boost to both confidence and ego.
"As coaches we can't do any more. After you have lit the touchpaper, all we can do is retire and hope they buzz."