Neville announced on Tuesday morning that he is to depart the Merseyside outfit - who he joined from Manchester United in 2005 - when his current deal expires at the end of the season, stressing that he will be looking to continue his playing career elsewhere.
In June, the 36-year-old will work as part of Stuart Pearce's England Under-21s backroom staff at the European Championship in Israel, having previously done so for the Young Lions' qualifier against Belgium in February 2012.
And former Everton defender Andy Hinchcliffe believes Neville may well take on some coaching duties at whichever club he plays for next.
"When he moves on, I would not be surprised if it is not all about playing for Phil," Hinchcliffe told Sky Sports News. "He wants to play for another two or three years and if he is fit enough to do it, then great.
"But I think he will start to think about the coaching side of things, especially with him being away in the summer in Israel with England Under-21s."
Neville, in a statement released to Press Association Sport, said: "It's been an honour to play for and captain Everton Football Club. I've thoroughly enjoyed my time on Merseyside and will leave with immense pride.
"I would like to thank the manager, chairman, all of the staff and the players at Everton for their continued support during my time at the club.
"I'd also like to pay a special thanks to the fans, who have been amazing over the past eight years and Everton will always have a place in my heart.
"I want to continue to play at the top level as long as I physically can, and will be weighing up my options before making a decision on my next move. I'll now be doing everything I can to help Everton finish as high up the league table as possible."
- Sports & Recreation
- Andy Hinchcliffe