City, Arsenal and United are currently all in the top-four spots in the Premier League table as things stand, and Neville believes that they will stay in the Champions League qualification places.
The former Manchester United defender also predicts that fourth spot will be a fight between Liverpool, Chelsea and Tottenham Hotspur, with current league-leaders Leicester City dropping out of contention.
"I think City, Arsenal and United will finish in the top three, and I think it's between Liverpool, Chelsea and Tottenham for fourth, I don't think that's rocket science,” he said.
Tottenham are currently the closest team to the top-four, and they have gone unbeaten in their last 12 Premier League matches.
Liverpool, meanwhile, have started to show signs of encouragement under the guidance of Jurgen Klopp, and their 4-1 win over City in their most recent outing has increased talk of their chances of breaking into the Champions League spots.
Chelsea, on the other hand, have made an inauspicious start to their campaign.
The Blues are sat in the bottom half of the table, but their quality remains undoubted and it seems unlikely that they will continue to play so poorly for much longer.