Netherlands international Van de Beek became Ole Gunnar Solskjaer’s first signing of the summer last week and the Red Devils boss is now turning his attention to other targets.
Manchester United, who finished third in the Premier League last season and reached the semi-finals of the Europa League, have been linked with moves for the likes of Jadon Sancho, Jack Grealish, Alex Telles and Sergio Reguilon.
Neville believes his former club need to sign a left-back, a centre-back and at least one forward before the summer window closes on October 5, as they look to close the gap on defending champions Liverpool and rivals Manchester City.
Speaking to the Webby and O’Neill YouTube channel, Neville said: ‘I think the left-back area is important because Luke [Shaw] has had injury problems.
‘I think centre-back is critical and I do think at least one forward is important. I still think we need three or four signings.
‘I’ve got a feeling they [the Manchester United board] are on it and are just not getting them over the line quite as quickly as they’d want.
‘But they’re not panicking and they’re still in control I think. They’re not reacting to the market like they were a few years ago, they’re in control.
‘The signings are better, they’re a better age-profile and look like they will be at the club for a long time rather than a season or two.
‘I’m positive generally about United, but getting those players over the line is critical.’
After joining the Red Devils, Van de Beek said: ‘I cannot begin to explain how incredible an opportunity it is to join a club with such an amazing history.
‘I am now ready to take the next step in my career and perform at the highest level and there is no higher standard than Manchester United.
‘This team has some of the best midfielders in the world and I know that I can learn from them and also bring my own strengths to the group.
‘Having spoken to the manager about his vision for this team, the direction that the club is going in is hugely exciting and I cannot wait to be a part of that.’
Manchester United begin their 2020-21 Premier League campaign on Saturday, with Crystal Palace making the trip to Old Trafford.