The 21-year-old has won two caps for the national side, but he has fallen out of favour after a lack of first-team football at Old Trafford.
"I signed for a couple of years at United so the goal is to do my best here for the season and go back and make sure I get back into the team and the England set-up," The Mirror quotes him as saying.
"It is just great to be playing again. There is nothing like being out on the pitch and the crowd singing your name. It was a bit frustrating. What am I doing if I am not playing?
"I know how everything works here and the gaffer just wants to give me game-time and wants me to improve so I am just glad I am back."
Zaha has played twice since his return to Palace and scored a last-minute equaliser in the 3-3 draw against Newcastle United at the end of August.