"I think obviously with the naming of Pako as the manager I will be leaving the club and looking for other opportunities," Neville was quoted as saying by British media.
"It's football. Hopefully in the future when I am a manager, I will want to bring my own staff with me.
"That is the case now and it's time for me to leave Valencia and to grab hold of other opportunities that are going to come my way. It has been a fantastic year."
Neville, 39, joined Valencia last July to work under then manager Nuno Espirito Santos, who was subsequently replaced by Neville's brother Gary in December 2015.
A turbulent season saw Gary Neville depart after just four months, while his younger brother Phil stayed on as Ayesteran's assistant. Valencia went on to finish 12th in La Liga.
"In terms of my overall development as a coach, hopefully a manager, and as a person, I cannot think of a negative about the whole situation," said Phil Neville, who is due to complete his UEFA Pro Licence to be qualified to manage in a few weeks' time.
Before joining Valencia, Neville was an assistant to David Moyes at Manchester United, where he spent most of his playing career, but now wants to strike out on his own.
"You've got to do your process, do all your work and learn about how to be a manager. I am still learning, I am still young in terms of managerial experience, but the last three years I've gathered a lot of information, he said."
(Reporting by Neil Robinson; Editing by Ken Ferris)
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