Victory over United at the Etihad Stadium would put them on top of the table on goal difference from their rivals and they go into the game as the only unbeaten side in England's four divisions.
"Roberto Mancini deserves more time but it is not a ridiculous suggestion to think City would not consider making a change if he doesn't win the league," said Neville at a Football Writers' Association Forum in Manchester.
"Whilst he continues to be successful he should stay in his job but it does feel like one day (Jose) Mourinho or (Pep) Guardiola will end up there.
"They have a new chief executive and a new director of football who presumably have the ear of the owner.
"It might be three or five years but eventually they will want to stamp their mark on the club and Mourinho and Guardiola have to be pretty high on the list."