Manchester United boss Mourinho is under pressure to deliver at Old Trafford after two mediocre seasons.
Tottenham counterpart Pochettino is among the favourites to take over the Red Devils if Mourinho fails to steer the club to silverware this season.
Mourinho has tried his best to shape a Manchester United team into his own, offloading the deadwood from the Louis van Gaal days in favour of signing powerful players such as Romelu Lukaku, Paul Pogba and Eric Bailly.
But Neville thinks Pochettino would sign young, robust players capable of carrying out his orders on the pitch.
The former United star told the Second Captain’s podcast: “Ajax, Manchester United and Barcelona are the three bastions of European football in terms of style of play.
“United have always played 4-4-1-1, 4-4-2, with two wide players.
“It’s ingrained in the club. Don’t change, don’t make short-term decisions.
“The fans weren’t happy, the stadium was starting to have empty seats and then they think, ‘right, we need to win’ and they bring in Jose Mourinho, who likes powerful, robust, strong players.
“Out went nearly all those 11 and Mourinho brings in Lukaku, Matic, Fred, Bailly, a wave of players who suit his style.
“Mourinho is happy to sit back a bit deeper and have a more robust, physical player. As a Manchester United fan it’s painful to watch.
“Let’s say Mauricio Pochettino comes in next – he likes hungry 23, 24-year-olds, he likes pushing up the pitch and playing high, he likes players who can press from the front.
“How many Manchester United forwards do you see that run about like the Tottenham ones?”
Meanwhile, BBC Sport pundit Alan Shearer thinks United will axe Mourinho if he keeps criticising his players.
The 55-year-old has cut a sullen and frustrated figure so far this term, taking shots at the likes of Pogba, Antonio Valencia and Anthony Martial.
Mourinho left Chelsea and Real Madrid after high-profile fallings out with the likes of Eden Hazard, Cesc Fabregas, Cristiano Ronaldo, Iker Casillas and Sergio Ramos.
And Shearer said: “We’ve learnt from the past that, if he takes too many players on like he did at Chelsea and Real Madrid, then there’s only one thing that will happen.
“If he upsets too many players because of his way then ultimately he will lose his job because the players, more often than not, win.
“They’re the ones with the power now, unfortunately.”