Former United skipper Neville, who retired last season, believes defender Jones - a £16million buy from Blackburn - has the leadership qualities to lead the team at Old Trafford.
"I think this lad's going to be a star, I really do," said Neville.
"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."