United forked out over £200million on new signings last term, which helped Ole Gunnar Solskjaer guide them to a third-place finish in the Premier League.
Solskjaer is yet to bolster his squad in the current transfer window, although reports suggest a £40million deal for Ajax midfielder Donny van de Beek is close to completion.
Yet Neville believes United still need to strengthen in a number of areas, urging his former club to make four or five signings this summer.
“The Manchester United squad, as it stands today, cannot challenge for the Premier League title this season,” the Red Devils legend told Sky Sports.
“The squad needed four or five improvements and it still needs four or five improvements. I've been saying that for a year and I've even nominated the positions I feel they need to improve.
“They have to sign a world-class centre-back. For me, another midfield player. I also think a right-winger, a centre-forward and you have to look at left-back because of Luke Shaw's injuries and the fact he has obviously been in and out of the team in the last two or three years.
“So, I think there are definitely four or five players required and to not get three I think it would be a problem because of what the other clubs are doing.
“If Liverpool get Thiago, if Manchester City do what they are looking like they are going to do and with Chelsea doing what they've done, they are your competitors and they all look like they are improving and moving forward.
Get the latest transfer news straight into your inbox!
Want to be on the ball with Jadon Sancho to Manchester United updates? Or perhaps you're a Chelsea fan wondering who on earth could join next?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“So, United have to do business but I do believe more in the strategy of what's happening, they just have to get the deals over the line.
“That's not always easy but they have to try and do it quickly to give Ole the time to build to get this team moulded for the start of the season.”