The United hierarchy are reportedly considering Van Gaal's position at Old Trafford amid a six-game winless streak, headlined by three consecutive defeats after Saturday's shock 2-1 loss at home to Norwich City.
Jose Mourinho has been tipped to replace Van Gaal at Old Trafford since he left Chelsea last week, with many associated with the side hungering for a return to the old glory of Ferguson's trophy-laden 27-year spell there.
But Neville - now an assistant to brother Gary leading Valencia in La Liga - said sacking the Dutchman will not automatically mean success, adding that that is not the answer.
"It's not the Sir Alex Ferguson era now; that time has gone and there needs to be a reality check," Neville told BBC Radio 5 live.
"It's the Louis van Gaal era. Constant change is not the answer."
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United are fifth in the Premier League on 29 points, only outside the top four on goal difference, while they are nine points adrift of surprise leaders Leicester City heading into Christmas.
Neville added: "I was at United as a player for nine years and it wasn't pretty every week.
"There seems to be an obsession at all clubs now, if you don't get the right results in four or five games then it's time to change the manager. That is not the answer.
"There is talent in the team. United are only a few points off the top three, it's not all doom and gloom but performances must get better.
"They need to put faith in a man who has won trophies in every major European country. United asked him to get into the Champions League, and he did, now this year is about winning a trophy.
"He has the experience, he can handle being at Old Trafford and people need to relax about constantly needing to change and sack managers.
"United have to make a decision. Do they turn into a club who changes manager every 12 to 18 months or do they look for stability?"