The 20-year-old signed for the Premier League champions in January for a fee of £17 million but went straight back on loan to the Eagles.
Zaha is excited by the prospect of linking up with Old Trafford's many superstars, but is determined to fight for his place and claim a starting berth.
"I am just anxious and excited," he told The Sun. "I cannot wait. It will be something different. When I walk into that dressing room at United, I do not know what I will feel. I will keep my head down as I am there to play football.
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"I have to be patient. I do not expect to walk in and play week-in week-out. Once I get the chance I will take it."
Zaha's current club, Palace, are in fifth place in the Championship and locked in a tight battle to secure a play-off spot, though their form has suffered since the winger agreed to move to United.
But the Ivory Coast-born attacker is adamant his only priority right now is promotion, and is determined to help Palace reach the Premier League before he leaves.
"At the moment, though, the priority is Crystal Palace," he continued.
"I can only assure everyone this is the case. I've had a little dip in my performance since I signed for United, I will not deny that. But I have to get back to what I do well.
"People are saying it is the speculation of going to United which saw me struggle. But Van Persie went 10 games without scoring but it was one of those things. He was still doing his best and playing a part. Equally, I am desperate to get Palace up.
"All I can do is keep my head down. I have to try to cope with this success, while doing my best for Palace until the end of the season."