Sanchez has been linked with a move to Premier League rivals Manchester United when his contract expires at the end of the season, while Manchester City targeted the Chile international during the summer but a move fell through after Arsenal could not line up a replacement.
Former United defender Neville believes Jose Mourinho's side should always compete to sign the best players in the world but he has not been impressed with Sanchez's performances so far this campaign.
"Sanchez has been distracted at Arsenal for the last six months," said Neville.
"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."