Barcelona have announced a deal to sign Atletico Madrid midfielder Arda Turan.
Crewe have signed midfielder Billy Bingham from Dagenham
The 36-year-old former Blues skipper has not ruled out continuing his playing career, although he has also been linked with a role as part of the coaching setup at Manchester United under former Toffees boss David Moyes.
The former United player, who has not played since early March because of a knee problem, could also be tempted to follow his brother Gary into media work.
"I have not made a decision yet - I have not officially retired yet," Neville told the official Everton website.
"Over the next couple of weeks that is the main decision I have to make; whether my body is up to the physical demands of Premier League football. I will sit down with my wife and family and come to that decision.
"I have thought about it but I will take a couple of weeks and have a holiday, then make the decision.
"I am looking forward to the next challenge in my career. It has been a tough season but one of the most enjoyable.
"I am in a position many people would love to be in. I am coming to the end of my football career and I have got many options.
"I have been preparing for this moment for a number of years. I will take the next couple of weeks to wind down and mentally rest after a hectic couple of weeks. Then I will make my decision and I back myself to make the right decision."