Neville was speaking on Sky Sports after Manchester City said they were “aware of a video circulating on social media which appears to show a supporter making racial gestures” during their match against Manchester United.
The club also said they are “working with Greater Manchester Police in order to help them identify any individuals concerned”.
The alleged incident occurred in the second half of City’s 2-1 defeat at the Etihad as a supporter appeared to make a monkey gesture towards a United player.
Speaking on Sky Sports, Neville said: “You are watching the Prime Minister’s debate last night where he is talking about migration to this country, and people having to have certain levels.
“It fuels it all the time. It has got worse over the last few years in this country and not just in football.”
A City statement after the game read: “Manchester City FC are aware of a video circulating on social media which appears to show a supporter making racial gestures during the second half of the match against Manchester United this evening.
“Officials from the club are working with Greater Manchester Police in order to help them identify any individuals concerned and assist with their enquiries.
“The club are also working with GMP regarding an instance of objects being thrown onto the field of play.
“The club operates a zero tolerance policy regarding discrimination of any kind, and anyone found guilty of racial abuse will be banned from the club for life.”