The 30-year-old United States international has had two spells with the Goodison Park side in the last couple of years - and Neville wants him to join permanently.
He told Sports Illustrated: "If there is a chance, I make sure that I try (to tempt him to Everton) every time I speak to him.
"That's the first thing I say to him. Toward the end of his spell back in January I even tried to kidnap him for a while and keep him in England!
"I'm telling the truth here when I say the last two times he's been over he's totally transformed our season.
"He's the ultimate professional, he's got great quality, and the Everton fans love him.
"He's a hero at Goodison Park, and he's played less than 20 games for us. I've played with some world-class right-sided players in my time, and he's up there with them."