The 28-year-old is out of contract at the end of the current campaign and has refused to sign a new deal, while his attempts to force an exit from the club over the summer proved fruitless.
Having missed the first few games of the season due to injury, the Chilean has now gradually begun to return to action, but Neville thinks that his apparent lack of enthusiasm for the Gunners' cause is evident on the pitch.
"Sanchez has been distracted at Arsenal for the last six months," he told Sky Sports News. "His career at Arsenal, I couldn't say a bad word about him until two or three months before the end of last season. I did feel he became distracted. Let's see how he performs this season at Arsenal.
"Ultimately he is still building up his fitness, he's still not in the team. What I saw from Arsenal [against Chelsea] on Sunday was a performance that I liked, and I've not said that too often about them in big games over the last four or five years. Sanchez wasn't on the pitch; Alex Iwobi and Danny Welbeck were playing [up front].
"What it showed for Arsenal on Sunday was that if you get players who work together and stick to a game plan, you can perform, sometimes better than with players who have got more talent.
"Sanchez has always been a hard worker. He needs to get back to doing that for Arsenal first because they've got big games coming up."
Meanwhile, reports in Spain today have suggested that Manchester United have entered the race to sign Sanchez next summer and could tempt him to move to Old Trafford with a £25m signing-on bonus.