The England international has struggled with injuries over the past two seasons and has seen his opportunities limited.
Wes Brown, John O'Shea and Rafael Da Silva are all options for Sir Alex Ferguson at right-back, with O'Shea getting the nod in the UEFA Champions League final.
Neville has even been linked with a shock move away from Old Trafford, with Middlesbrough considering a bid for his services, but the veteran is keen to stay with the Premier League champions.
The defender admits he has had to change his game in recent years and accepts he may not be able to offer the same attacking threat as some of his team-mates.
Important roleHe told the People: "I played a good number of games last season and I hope that continues next season because playing for this club is as special to me now as it was when I first pulled on the shirt as a schoolboy.
"Full-backs have an important role, particularly at United, in terms of the way we attack and the way in which there's a transition from defence through our full-backs to attack.
"We have always set up play and been part of the extra-man situation and we always play with width.
"The way you see guys like Patrice Evra and Rafael Da Silva attacking, they are more like wingers who can defend - they aren't just full-backs any more.
"The way in which the modern full-back like Rafael, his brother Fabio and Patrice play is fantastic to watch. Before I got injured a couple of years ago you'd say I was running forward nearly all the time during the game.
"Don't get me wrong - I don't do that in the same eye-catching way as they do, but you understand the changes and development in the game and the way I've had to adapt."