The 20-year-old, who was signed by Sir Alex Ferguson back in January before being loaned back to Crystal Palace for the remainder of last season, has been linked with another return to the newly promoted Selhurst Park outfit.
However, Moyes has been quick to stress that the England Under-21 international attacker will have time to try and make an impression under his new regime.
|MANCHESTER UNITED LATEST
|2/1||Manchester United are 2/1 with Coral to retain the Premier League
"I'll have a look and see how he goes.
"This football club has a great record of producing young players and bringing in young players and we hope Wilfried is another one we can push forward."
Wayne Rooney's future has also been the subject of recent speculation, despite Moyes' repeated insistence that the England international is going nowhere.
Moyes, who engaged in a legal battle with Rooney in 2006 over comments made in the striker's autobiography having worked together previously at Everton, reiterated that the 27-year-old will not be sold and insisted that the pair have a strong relationship.
"The club have said that Wayne is staying, and he’s not for sale," he added.
"I’ve met him on several occasions recently. Wayne has been to my house, I’ve been to his and obviously we’re here [at the training ground] every day. A lot has been said about me and Wayne over recent years but we have a good relationship.
"He’s trained great. They [people at the club] are telling me they’ve never seen him in better shape. That’s positive. He’s not for sale and I will try to get the best Wayne Rooney I possibly can."