Veteran Ryan Giggs has been appointed as interim manager for the club's remaining four games in charge, while ex-United players Nicky Butt and Paul Scholes have been called upon to assist the Welshman.
Neville, who works as an England coach, has been focusing on his punditry work for Sky Sports, but Chadwick believes that the former United captain could be tempted by a role at Old Trafford.
"If he was given the opportunity to manage the club, I think it's an opportunity he would definitely have to consider taking," Chadwick told talkSPORT. "The pull of going to Manchester United would be too great to turn down."
Moyes lasted less than 10 months after he was appointed as Sir Alex Ferguson's successor.