With Ibrahimovic back from injury, many supporters have called for the 24-year-old to be replaced by the veteran Swede, but former United defender Neville does not have any concerns about Lukaku's role as Jose Mourinho's first choice attacker.
"I don't think Jose Mourinho will be worried about Romelu Lukaku's lack of goals, but I think ultimately he's got two big games coming up," Neville wrote in his Sky Sports column.
"He was brought in to score goals in the games which United were drawing last season. However, it is in the big matches where they now need him most. If there is a way to get at Arsenal and Manchester City then it is by really going at their defences.
"Lukaku gets more chances created for him but he's also under more pressure, so misses get scrutinised, and rightly so, but these are the games where he can silence his critics.
"I don't see Zlatan Ibrahimovic as a threat to Lukaku at all but as a supplement. The only way Ibrahimovic can become number one is if the aura of Zlatan gets to Lukaku.
"Zlatan is confident but Lukaku is number one, the fans and the manager believe in him and if he does have any demons then he needs to clear them from his mind."
Manchester United travel to London to face Arsenal on Saturday, December 2, before home games against CSKA Moscow and Manchester City in the following eight days.