The 37-year-old, who had a 10-year playing stint with United up until 2005, returned to Old Trafford last summer in the role of first-team coach under David Moyes.
However, when asked by Sky Sports News about his future, Neville replied: "[Van Gaal has] got massive experience from coaching some of the biggest teams in the world. He comes with a fantastic pedigree. It's the first foreign manager that Manchester United have had, so it's interesting times ahead.
"We've got to make sure we improve upon last season and hopefully with a new manager we can get back to challenging for titles and European medals.
"I hope [that I will stay]. It's business as usual as far as I'm concerned. I was first-team coach last year, but I'm not sure what my role will be next year. Over the next couple of weeks I'll find out about my role and hopefully I will be involved at Man United."