The former Manchester United captain feels a set of rules similar to the transfer window for bosses would represent a positive step, providing coaches and players with more certainty.
Neville believes there would be backing for the idea from those within football, but does not think owners would be happy.
The ex-Valencia boss was speaking after Middlesbrough made Aitor Karanka the sixth Premier League manager to lose his job since the start of the campaign.
"I would support completely the idea that managers can't be sacked during the season," Neville said.
"When you set off at the start of the season with a manager then he has to be your manager for the entire season.
"Football would support it, in terms of the professional side - I'm not sure whether the owners would.
"But it would mean the players would know you're going to be the manager until the end of the season, they'd have to get on with it."
Despite Leicester City's improvement since sacking title-winning manager Claudio Ranieri, Neville insists there are plenty of examples where such a move does not pay off.
He continued: "Teams are making changes at the bottom of the league and I'm almost sitting there thinking, 'I wish this doesn't work' because when it does, it gives others the confidence to change their manager.
"There have been examples where it's worked when managers are sacked and where it hasn't. I'm not sure there is a distinction between either.
"It seems to be more the done thing where you do sack the manager at the earliest point as the players respond. We have seen that at Leicester - what an incredible bounce they have had. It's happened at Swansea and Hull."
Former Liverpool defender Jamie Carragher, who like Neville now works as a television pundit, has also previously supported the idea of preventing managerial changes mid-season.