The 36-year-old's current contract expires in June and he is yet to open talks with the club about a possible extension.
The former England international has already started 20 matches this season and but given his age and the fact he has recently undergone knee surgery, he remains unsure as to whether he can continue for another campaign.
"I'm quite relaxed about the situation," Neville told the Liverpool Echo.
"I spoke to the manager before Christmas and he asked me what I wanted to do. And I said I wanted to speak probably more towards the end of the season.
"I think I'm a year older than Sylvain Distin (who has just signed a year's extension).
"I think it's sensible at my age to first, see how the body is, and then see how my situation is within the club and at the end of the day ask 'Do I still retain the hunger and the determination, and more importantly am I still having a positive effect on the team?'
"These are the things over the next three or four months that I'll be weighing up and we'll take it from there.
"I've been at Everton for the last eight years and I've been captain and I've been a large part of what's been going on.
"But I want to remain as influential and if felt I wasn't as influential or I felt my form had dropped, or if I was standing in the way of someone who was coming through then I would have to look at it.
"That's the reason why I'm in no rush."