Barkley rejected a move to Chelsea during his medical in London last night.
The Blues and Tottenham were in the hunt for Barkley, 23, this summer.
And pundit Neville says the England international may have been promised a move to Spurs in January, resulting in the midfielder snubbing Chelsea.
“Ross is a homebird,” Neville told Sky Sports.
“I don’t know the ins-and-outs of it at this moment in time.
“He might have got down there and thought ‘hang on a minute, I love Everton‘.
“Or it may be another club that he wanted to go to more has told him to hang on for five months and they’ll sign him in January.
“Maybe Tottenham or someone else. They may have put some doubt in his mind.
“It’s a strange one. Once you go for a medical, it’s very unusual you’ll change your mind from there.
“I can’t imagine the physio or sports scientist has put him off.”