"At the age of 26, you always have to think that there's more to come," Neville told BBC Radio 5 live.
19 Oct 2002
- Scores winner in Everton's 2-1 victory over Arsenal
13 Feb 2003
- Makes England debut in 3-1 defeat by Australia
17 June 2004
- Scores twice in England's 3-0 win over Switzerland at Euro 2004, but his tournament is curtailed by a broken foot
31 Aug 2004
- Joins Manchester United from Everton in deal worth £27m
28 Sept 2004
- Makes United debut, scoring hat-trick in win over Fenerbahce
1 July 2006
- Sent off as England lose on penalties to Portugal in World Cup quarter-final
- Wins first of four Premier League titles with United
21 May 2008
- Part of the United team that wins Champions League, defeating Chelsea on penalties in the final
- States intention to leave Old Trafford before signing a new five-year contract
12 Feb 2011
- Scores overhead kick in win over Manchester City, his "best goal so far"
7 Oct 2011
- Sent off as England draw with Montenegro to qualify for Euro 2012
11 Feb 2012
- Marks 500th senior game by scoring both goals in United's 2-1 win over Liverpool
12 Oct 2012
- Captains England in 5-0 win over San Marino, scoring twice to go fifth on all-time goalscorers list
"We need to see Wayne Rooney improve and he needs to see himself improve."
Neville, now an England coach, added: "He's a wonderful player, one that is at his best when he's like the street kid; fighting for every ball, taking every free kick, every throw-in, tackling and heading, fighting to win."
The former England right-back also pointed to the examples Rooney can learn from in the Old Trafford dressing room if the 26-year-old is to further his game.
"Paul Scholes and Ryan Giggs have adapted their games," said Neville, who won eight Premier League titles, three FA Cups and the Champions League with United.
"Ryan Giggs has gone from a flying left winger to someone who now plays off the front at inside left as well as central midfield.
"Paul Scholes was a goalscoring number 10 player when he first started as a 16-year-old, now he's a holding midfield player who controls the game.
"You have to adapt. Rooney is still a centre forward, but he'll adapt over the next 10 years to become someone who's thought of in that same way as those two players."
Rooney had already netted his first senior goals in Everton's League Cup win over Wrexham, but it was his long-range effort to end the Gunners' 30-match unbeaten run in October 2002 that propelled him into the spotlight.
At the time,
Arsenal manager Arsene Wenger said:
"Rooney is the biggest England talent I've seen since I arrived in England. There has certainly not been a player under 20 as good as him since I became a manager here."
Four months later in February 2003, Rooney became the then youngest England international when he made his debut in the
3-1 defeat by Australia.
Since then, he has won four Premier League titles, two League Cups and the Champions League with Sir Alex Ferguson's side.
"These 10 years have gone well, I've been successful, winning trophies at club level," said Rooney. "The only thing missing is to be successful and to win things with England.
"I haven't been at my best for England, that is something I'm desperate to put right."
Despite moving fifth on England's all-time goalscorer list with two strikes in Friday's win over San Marino, Rooney's disappointment with his international record could stem from his poor showing at major tournaments.
"He's an excellent player," said Hodgson. "Like all players in England that reach the heights, the likes of Steven Gerrard, Frank Lampard, John Terry, they come under enormous scrutiny and people forget how good they are.
"Despite his young age he's been a great servant to the country and I think we might be grooming him to be captain well into the future."
You can hear more on Wayne Rooney's 10 years in the Premier League in a Monday Night Club special on BBC Radio 5 live from 22:00 BST on Monday.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.