United boss Jose Mourinho is thought to be in the market for a new defensive midfielder to share the workload with 35-year-old Michael Carrick, allowing Paul Pogba to play in a freer role further forward.
Chelsea's Matic is among the leading targets for the Red Devils, and Neville believes that the Serbian would be a good fit at Old Trafford.
"Michael Carrick has obviously got one more year but he can't play every single week so they do need to have that player who can come in and do the same job, and Nemanja Matic would be able to do that. So I think United do need a holding midfield player," he told Sky Sports News.
"Morgan Schneiderlin was let go earlier in the season and Bastian Schweinsteiger didn't get a game. So you're talking about there needing to be a replacement for them and ultimately Matic would fit the bill.
"It's a strange one for Chelsea to let him go because I thought he was really good for them with [N'Golo] Kante. I think they need to strengthen, so I'm not sure why they're letting him and they must have a replacement."