Mancini finds himself under pressure heading into Sunday's Manchester derby, more because of their failures in the Champions League than on the domestic front.
Victory over United at the Etihad Stadium would put them on top of the table on goal difference and they go into the game as the only unbeaten side in England's four divisions. But combining their European troubles with the recent arrival of chief executive Ferran Soriano and director of football Txiki Begiristain, Neville feels Mancini's position is anything but secure.
"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." Neville also believes Sir Alex Ferguson will continue as United manager for some time and does not feel the possible departure of Mourinho from Real Madrid this summer will hasten his exit.
"Whilst he wants to carry on, Sir Alex will not stand aside for anybody. He will decide when he doesn't want to do it anymore," Neville added.
"He is not the type of person who would just step aside so he could watch someone else manage his football team. It has been Alex Ferguson's last season for 15 years now.
Unless it is the best kept secret in the world, nobody knows other than him."