The defender had surgery in May and is gradually easing himself back into pre-season training.
"It has actually been fantastic," said Neville, who is with the squad on their tour of Australia but not yet fit enough to feature in Saturday's first game against Sydney FC.
"It's been nine weeks now (since the operation) and at eight weeks I was allowed to start running.
"This week has been more of me slowly settling back into training.
"I have been doing one session a day with the team and another session in the gym to keep the strength up in the knee.
"As pre-season gets closer to the full season I will step up my training.
"I feel really fit, really strong, and for the first time in months I am running without pain in my knee, which is a great sign.
"There are three games this week and it would be great to take part in some of them and get some minutes under my belt."
Injury may force new striker Jermaine Beckford to miss out on his Everton debut on Saturday.
The centre-forward, signed on a free transfer from Leeds, has a slight leg injury which could keep him sidelined.