Jones' £16 million transfer from Blackburn Rovers to Old Trafford will be finalised on July 1 and Neville predicts that the centre-back, who can also play in midfield, will skipper the side later in his career.
“I think this lad’s going to be a star, I really do,” Neville told The New Paper in Singapore.
“I think he’s going to be somebody who could potentially be a captain of Manchester United in the future. He looks really solid and he’s somebody who can be a huge player for the club for the next 10 years.
“There’s a lot of potential there and the performances he’s put in over the last two years have been outstanding, particularly against us. For a 19-year-old that’s excellent. He’s a great signing for us.”
Neville also believes that there will be at least one more arrival at Old Trafford this summer.
He continued: “I think the manager will sign a central midfielder because of Owen Hargreaves leaving and Paul Scholes retiring.”
Wesley Sneijder has been strongly linked with a move to Old Trafford. United are also one of many clubs reportedly interested in young Barcelona midfielder Thiago Alcantara, but the Spaniard only recently signed a new long-term deal with the European champions.
Neville made 602 appearances for United before retiring last season.