The Chilean failed to secure himself a move away from the Emirates Stadium over the summer, with the deadline passing without the Gunners cashing in on a player in the final year of his contract.
Manchester City had led the hunt for his services, with a £60 million offer on the table, but recent reports have suggested that Jose Mourinho is also mulling over an approach for the 28-year-old.
Neville believes such a move would make sense, with a club of United’s stature and ambition needing to be in the market for the cream of the global crop.
The former Red Devils defender told Sky Sports News: “I’ve not seen the Alexis Sanchez news, so you have given me something I haven’t heard before, but, from that point of view, United, from a general perspective, should always be challenging for the best players in the world and bringing them in.
“Sanchez has been distracted at Arsenal for the last six months.
“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.”
Sanchez was used from the start by Arsenal in their Carabao Cup victory over Doncaster on Wednesday.
He has, however, been restricted to bench duty in the Premier League since seeing the summer transfer window close.
As a result of seeing limited game time, a man who netted 30 times for the club in all competitions last season has just one Europa League effort to his name this term.