Cole urged the promising winger to learn from Ryan Giggs if he wants to establish himself at the Premier League champions.
He told the Sunday Mirror: "Zaha has come in, put a good shift in pre-season and now David Moyes can make his mind up from there.
"Everyone starts from a clean slate so to speak, as it's a new manager with new ideas and he's going to pick the team that he thinks can win the championship.
"So I think Zaha is going to get a good opportunity and that is why he has come to Manchester United in the first place.
"But he's just got to come in and enjoy the experience because he's playing with some quality players and he will learn from them.
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