Bright, now academy coach and a close friend of chairman Steve Parish, said Zaha would leave with the club's blessing as long as they received a "fair price".
He told the Daily Mail: "If one of the big clubs comes knocking, it is difficult to hold them back but what the club says, and what every club should say, is that we want a fair price for the player.
"Steve has quite rightly said that if Wilf wants to go, then we won't stand in his way. But the club who are buying cannot put in an offer of half of what you rate him. Arsenal put in an offer for less than what the youngster went for when this lad is matured and is better now.
"When he went to Manchester United he probably wasn't ready. He is ready now. If someone wants him, come up with a good offer and Steve won't stop him. He would go with the club's blessing."