The Red Devils are in seventh place in the Premier League table following two victories in their last six outings.
Manchester United were 3-1 winners against Brighton at Old Trafford on Sunday thanks to goals from Andreas Pereira and Marcus Rashford.
The 20-time English champions have collected seven points from their last four Premier League games to suggest the Red Devils could be turning a corner.
But Solskjaer’s side have a long way to overhaul Leicester City and Chelsea FC in the top four given that Manchester United are 10 points adrift of the two clubs.
Former Manchester United defender Neville believes Manchester United need at least four or five new signings to allow Solskjaer to make further improvements to the squad.
“It’s been a really good month for Manchester United barring the Bournemouth defeat,” Neville told Sky Sports. “That game was frustrating and took us back a few steps but generally it’s been a better month than the one before.
“You can see some real excitement with Marcus Rashford, Anthony Martial, Mason Greenwood and Daniel James, there’s something to work on there.
“Defensively, with Harry Maguire and Aaron Wan-Bissaka, there’s something to work on there too. The young boy Brandon Williams gives me a great deal of hope.”
Neville added: “Look, Manchester United need four or five players with real quality and experience.
“They need another centre-back, they need a left-back and a couple of central midfielders and a striker or a forward. That’s not going to change and won’t change entirely even after January. But there’s something there.”
Manchester United appointed Solskjaer as their new manager last season after Jose Mourinho’s side lost 3-1 to Liverpool FC at Anfield back in December.
Solskjaer was initially appointed on a temporary basis before the Norwegian head coach was given the role full-time.
Manchester United are in seventh position in the Premier League table following their 3-1 win against Brighton.
The Red Devils are looking to improve upon their sixth-placed finish last term.
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