After consecutive Premier League defeats to Brighton and Tottenham respectively, calls have been made for Mourinho to become the third managerial casualty since the retirement of Sir Alex Ferguson.
Under the guidance of Mourinho, the club has failed to challenge for the Premier League over the past two seasons, despite his incredible record of success at his former sides.
The current status quo with run-ins with key figures in the squad and his recent rants with journalists has come under the microscope but Neville believes the club need to support the under-fire coach.
"We saw Louis van Gaal sacked after an FA Cup final victory, we saw David Moyes sacked with four games to go of a season, so we are no longer talking about a football club that is behaving as it has historically done," he told Monday Night Football.
"I accept these are different times and I accept the difficulties and challenges, but my honest view as I stand here now is that Ed Woodward gave him a contract last season, only seven or eight months ago, and he should see that contract through to the end and do the job.
"You can't keep jumping around with managers. I hear the third-year Mourinho stories and all the rest of it and you can't disagree with those stories because there is some history.
"But what I would say is it's time now for Manchester United to batten down the hatches and for Jose Mourinho and Ed Woodward to sort themselves out if there is a problem there.
"He saw the end of his contract at Inter Milan, he saw the end of his contract at Porto and he saw the end of his contract at Real Madrid," Neville added.
"It's only at Chelsea, which is a club of madness, where this has happened. At Inter Milan, Porto and Real Madrid he saw it to the end so let's not rewrite history. At Chelsea, everybody dies a little bit early. It's that type of club, he's not on his own there.
"It was tough for him at Real Madrid and he got through to the end of the season. I don't see it happening during the season.
"To suggest that Manchester United are like Chelsea is not right. I have to say Manchester United still do things slightly differently."