The 20-year-old scored his first goal for the club in Friday's 2-2 draw with Cerezo Osaka and says he wants to be in the first team squad this season
United acquired the 20-year-old from Crystal Palace in January of this year before immediately loaning him back for the remainder of the 2012-13 campaign.
He went on to play a prominent role in the club's promotion to the Premier League via the play-offs and has subsequently been strongly linked with a second temporary stint with his boyhood team in the English top flight.
However, after scoring his first goal for United during their 2-2 draw with Cerezo Osaka on Friday, Zaha has underlined his desire to make an impact in his debut campaign at Old Trafford.
"My own target for my first season in Manchester is to be able to get minutes," he said. "I don't want to go out on loan or anything. I just want to play when I get the chance."
The one-cap England international also insisted that he is not phased by the prospect of competing with the likes of Ashley Young, Nani and Antonio Valencia for a starting berth.
"That is the gamble I had to take," he added. "I am prepared to take that gamble. I enjoyed my time at Palace but I am at Manchester United now.
"There are bigger players than me here, so getting minutes will just do me fine."
New United boss David Moyes also lauded the winger following his positive contribution in the pre-season friendly clash with Cerezo.
"Wilfried has done well," he said. "He has been quite quiet because he is still getting to know everybody, but he has had an impact in the games.
"We want to try and bring him along nicely. Tonight will help because he showed the players that he can make things happen.
"We want all players at Manchester United to score goals and he has come up with an important one."