The former defender believes that Allardyce will want to bring in his own players that he can trust.
Allardyce recently replaced Dick Advocaat at the Stadium of Light after the Dutchman decided to bring an end to his reign with his side sitting firmly inside the bottom three.
Many are now expecting Allardyce to once again perform fire fighting duties at another relegation threatened club, with him enjoying the record of having never been relegated as a manager.
Neville though, says he will have a fight on his hands with this current Black Cats side.
“This is his toughest [job], but he’s experienced and knows what he’s doing,” he told Sky Sports.
“They’re teetering on the edge now these Sunderland players. He’s got to get something out of them again this season. They’ve managed to do it the last few seasons, Advocaat, Poyet have managed to get something out of these players. He has to pick points up.”
The former defender has also anticipated that Allardyce will want to be active in the January transfer window to strengthen his squad.
Dick Advocaat was busy in the summer as he brought several new faces into his squad and spent relativey big to acquire them as well, but so far none of his summer recruits have managed to look like good signigns.
And Neville says Allardyce will be keen to add players he can trust to the squad knowing they are in for another relegation battle already.
“He will want to get a few of his own bodies in,” he added.
“[He will want] a few of his own people who he can trust and who are reliable around the Christmas and January time when the window opens, but he’s got to give them a chance by picking up points before then.”