Former Liverpool defender Jamie Carragher believes succeeding Amorim at United would be “an attractive job” for “any manager”.
“It’s one of the biggest clubs in the world and always will be,” he told Sky Sports.
“Imagine being the guy who gets it right. And someone sooner or later will get it right at United. The club is too big to consistently fail.”
But Neville believe it would be “clever” for the club to wait until the summer to name a permanent manager.
“I don’t think the manager pool is full right now in terms of great talents,” he said.
“Look at Chelsea bringing in Liam Rosenior. That is not what Chelsea are used to or should expect and that’s not being disrespectful to Rosenior.
“I am not sure where United would go but I think it’s clever to wait till the summer when maybe there will be more coaches available from other clubs and the World Cup situation.”
Rene Meulensteen, who spent six years as United’s first-team coach, urged the club to hire a replacement who knows how to win in the Premier League.
“They don’t want to make another mistake and very quickly go for someone that they’re sort of trying to fill the void with,” he told BBC Radio 5 Live.
“They need somebody with pedigree. Someone who understands the Premier League, who’s been successful in the Premier League.
“Someone with a strong personality, with charisma. Someone with good vision about how to take United forward.”
Former United goalkeeper Mark Bosnich added: “It should be about the club and the team doing well.
“Because right now, the supporters will be tearing their hair out because they want to know what’s going on and they deserve to know what’s going on. It’s a complete mess.”
