He has been heavily linked with Real Madrid star Gareth Bale and £48m-rated Inter Milan winger Ivan Perisic, as well as a number of full-backs, but United have been frustrated in their attempts ahead of the opening Premier League game of the season at home to West Ham on Sunday.
Neville also believes the sale will improve the players already at United, with Matic's new midfield colleagues set to benefit.
Matic won two Premier League titles, the FA Cup and the EFL Cup across two spells at Chelsea.
I can't think of a reason why Chelsea would sell him.More news: Alexis Sanchez to miss start of season through injury
Jose Mourinho's men could only muster a painful 1-1 draw in this fixture last season - a result reflective of their ongoing woes at home in the Premier League last season - and cannot afford to start off in the same way on Sunday. As you know the Premier League is the main target.
His final message to us that season was simple - enjoy your summer, bask in the glory, but be prepared to work when you get back, .
Matic made his competitive debut for United, in their 2-1 Super Cup defeat by Real Madrid on Tuesday night. "But they are very experienced and they also had some chances to score another because at the end we tried to go with everything to score and they had some counter-attacks".
"There is very rarely such big transfers between champions to clubs that are challenging them and it is a odd move". We are not happy that we lost but did everything. "But we can take a lot of good things from this game". "It's very important for confidence".More news: Markets slide, dollar slumps as North Korea fears spike
"That's our aim for this season and we have a very good squad".
Former Manchester United defender Neville didn't hold back in his criticism of Chelsea for their decision to sell an important player to their title rivals.
"I know it's hard because it's a European trophy and that's important for the club". We don't want to give away any competition.More news: Quake of magnitude 6.5 hits Indonesia's Sumatra; tremors felt in Singapore
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